a new technique for measuring spectral shape discrimination a new technique is described for studying the ability of listeners to discriminate between sounds on the basis of spectral shape a process called auditory profile analysis the advantage of the technique is that it reduces the range of the random rove in level necessary to provide a specified limit on the performance which listeners could achieve by level detection that is by employing a detection strategy based solely on comparisons of stimulus level thresholds were measured for the just discriminable ripple a pattern of alternating intensity increments and decrements in an equal amplitude multitone reference spectrum for a group of normal hearing listeners broadband high pass and low pass filtered conditions were tested the results indicated that the thresholds obtained using the new technique were well below the lowest level achievable by level detection referred to as the level detection limit in all conditions using a 20 db random within trial rove in overall level the lowest threshold occurred for the broadband stimulus while the highest threshold was observed for the most extreme high pass filtered condition the new technique appears to be well suited for study of profile analysis in hearing impaired listeners where stimulus bandwidth and rove range are limited

texture information in run length matrices we use a multilevel dominant eigenvector estimation algorithm to develop a new run length texture feature extraction algorithm that preserves much of the texture information in run length matrices and significantly improves image classification accuracy over traditional run length techniques the advantage of this approach is demonstrated experimentally by the classification of two texture data sets comparisons with other methods demonstrate that the run length matrices contain great discriminatory information and that a good method of extracting such information is of paramount importance to successful classification

working correlation structure misspecification estimation and covariate design implications for generalised estimating equations performance the method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations we investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods the asymptotic relative efficiency depends on three features of the analysis namely i the discrepancy between the working correlation structure and the unobservable true correlation structure ii the method by which the correlation parameters are estimated and iii the design by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes analytical and numerical studies of realistic data analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a gaussian estimation pseudolikelihood procedure is used with an ar 1 structure

improving power in small sample longitudinal studies when using generalized estimating equations generalized estimating equations gee are often used for the marginal analysis of longitudinal data although much work has been performed to improve the validity of gee for the analysis of data arising from small sample studies little attention has been given to power in such settings therefore we propose a valid gee approach to improve power in small sample longitudinal study settings in which the temporal spacing of outcomes is the same for each subject specifically we use a modified empirical sandwich covariance matrix estimator within correlation structure selection criteria and test statistics use of this estimator can improve the accuracy of selection criteria and increase the degrees of freedom to be used for inference the resulting impacts on power are demonstrated via a simulation study and application example copyright 2016 john wiley sons ltd

application of gee procedures for sample size calculations in repeated measures experiments derivation of the minimum sample size is an important consideration in an applied research effort when the outcome is measured at a single time point sample size procedures are well known and widely applied the corresponding situation for longitudinal designs however is less well developed in this paper we adapt the generalized estimating equation gee approach of liang and zeger to sample size calculations for discrete and continuous outcome variables the non central version of the wald 2 test is considered we use the damped exponential family of correlation structures described in munoz et al for the working correlation matrix among the repeated measures we present a table of minimum sample sizes for binary outcomes and discuss extensions that account for unequal allocation staggered entry and loss to follow up 1998 john wiley sons ltd

spectral shape discrimination by hearing impaired and normal hearing listeners the ability to discriminate between sounds with different spectral shapes was evaluated for normal hearing and hearing impaired listeners listeners discriminated between a standard stimulus and a signal stimulus in which half of the standard components were decreased in level and half were increased in level in one condition the standard stimulus was the sum of six equal amplitude tones equal spl and in another the standard stimulus was the sum of six tones at equal sensation levels re audiometric thresholds for individual subjects equal sl spectral weights were estimated in conditions where the amplitudes of the individual tones were perturbed slightly on every presentation sensitivity was similar in all conditions for normal hearing and hearing impaired listeners the presence of perturbation and equal sl components increased thresholds for both groups but only small differences in weighting strategy were measured between the groups depending on whether the equal spl or equal sl condition was tested the average data suggest that normal hearing listeners may rely more on the central components of the spectrum whereas hearing impaired listeners may have been more likely to use the edges however individual weighting functions were quite variable especially for the hi listeners perhaps reflecting difficulty in processing changes in spectral shape due to hearing loss differences in weighting strategy without changes in sensitivity suggest that factors other than spectral weights such as internal noise or difficulty encoding a reference stimulus also may dominate performance

the effects of amplitude perturbation and increasing numbers of components in profile analysis in a profile analysis task the effect of randomly perturbing the amplitudes of the components of multi tone stimuli was studied in two experiments in the first experiment thresholds for a signal added in phase to the central component of a standard were measured for different numbers of components in two conditions in one condition thresholds were measured in blocks for six different jagged standards and in another thresholds were measured when one of the six standards was chosen randomly on a presentation by presentation basis regardless of condition thresholds did not depend on the numbers of components and increased magnitude of perturbation increased thresholds moreover the slope relating thresholds to number of components did not increase with increasing magnitude of perturbation in the second experiment the signal consisted of an increase in amplitude of the central components and a decrease in amplitude of the outer components of the standard a stimulus type which has been shown to maximize the change in threshold with increasing number of components the amplitudes of component tones were selected randomly on a presentation by presentation basis thresholds fell with increases in the number of components but the slope relating thresholds to numbers of components did not change as the magnitude of perturbation increased the latter result contrasts with that reported by kidd et al j acoust soc am 90 1340 1354 1991

variation in spectral shape discrimination weighting functions at different stimulus levels and signal strengths this study evaluated whether weights for spectral shape discrimination depend on overall stimulus level and signal strength the degree of spectral shape change between two stimuli five listeners discriminated between standard stimuli that were the sum of six equal amplitude tones and signal stimuli created by decreasing the amplitudes of three low frequency components and increasing the amplitudes of three high frequency components weighting functions were influenced by stimulus level in that the relative contribution of the low frequency decremented components to the high frequency incremented components decreased with increasing stimulus level although individual variability was present a follow up experiment suggested that the level dependence was due to greater reliance on high frequency components rather than incremented components excitation pattern analyses indicated that the level dependence is primarily but not solely driven by cochlear factors in general different signal strengths had no effect on the weighting functions when normalized but two of the five listeners showed variability in the shape of the weighting function across signal strengths results suggest that the effects of stimulus level on weighting functions and individual variability in the shapes of the weighting functions should be considered when comparing weighting functions across conditions and groups that might require different stimulus levels and signal strengths

psychometric functions for level discrimination in cochlearly impaired and normal listeners with equivalent threshold masking the purpose of this study was to determine whether the form of the psychometric functions for level discrimination also known as intensity discrimination measured in a two interval two alternative forced choice paradigm changes with hearing impairment measurements of sensitivity d as a function of delta l 20 log p delta p lp where p is pressure were obtained in six listeners with cochlear impairments five normal listeners tested in the quiet and two masked normal listeners stimuli were chosen to encompass a wide range of conditions and difference limens results show that the d is nearly proportional to delta l over the entire range of stimuli this simple relationship is not changed by cochlear impairments or masking noise these findings indicate that if the transformation from stimulus intensity to decision variable is affected by hearing impairment or masking the change affects both the mean and the standard deviation in the same manner i e the standard deviation may be proportional to the derivative of the transformation as was suggested by zwislocki and jordan j acoust soc am 79 772 780 1986 the results also lend support to the notion that delta l plotted on a logarithmic scale is an appropriate representation of level discrimination performance

spectral weights for overall level discrimination in listeners with sensorineural hearing loss a conditional on a single stimulus coss analysis procedure b g berg j acoust soc am 86 1743 1746 1989 was used to measure the weight or relative reliance that normal hearing and hearing impaired listeners give to different frequencies in the discrimination of the overall level of a multitone complex on each trial two multitone tone complexes comprised of six octave frequencies from 250 to 8000 hz were presented to subjects the levels of the frequencies for each complex were randomly varied the listeners task was to identify the complex with the higher overall intensity level normal hearing listeners used a variety of listening strategies to perform the task showing no general preference to weight one component over another hearing impaired listeners however showed a general tendency to give greatest weight to the spectral information in the region of their hearing loss thirteen of the 14 hearing impaired listeners all of whom had a high frequency sensorineural hearing loss weighted one or more of the high frequency components in the complex the greatest

akaike s information criterion in generalized estimating equations correlated response data are common in biomedical studies regression analysis based on the generalized estimating equations gee is an increasingly important method for such data however there seem to be few model selection criteria available in gee the well known akaike information criterion aic cannot be directly applied since aic is based on maximum likelihood estimation while gee is nonlikelihood based we propose a modification to aic where the likelihood is replaced by the quasi likelihood and a proper adjustment is made for the penalty term its performance is investigated through simulation studies for illustration the method is applied to a real data set

the impact of covariance misspecification in multivariate gaussian mixtures on estimation and inference an application to longitudinal modeling multivariate gaussian mixtures are a class of models that provide a flexible parametric approach for the representation of heterogeneous multivariate outcomes when the outcome is a vector of repeated measurements taken on the same subject there is often inherent dependence between observations however a common covariance assumption is conditional independence that is given the mixture component label the outcomes for subjects are independent in this paper we study through asymptotic bias calculations and simulation the impact of covariance misspecification in multivariate gaussian mixtures although maximum likelihood estimators of regression and mixing probability parameters are not consistent under misspecification they have little asymptotic bias when mixture components are well separated or if the assumed correlation is close to the truth even when the covariance is misspecified we also present a robust standard error estimator and show that it outperforms conventional estimators in simulations and can indicate that the model is misspecified body mass index data from a national longitudinal study are used to demonstrate the effects of misspecification on potential inferences made in practice copyright 2013 john wiley sons ltd

observer efficiency and weights in a multiple observation task a sequence of seven tones sampled from one of two distributions differing in mean frequency is presented to observers who try to report which distribution was sampled estimates are obtained of the weight or importance given to each tone as a function of its temporal position in five experiments the reliability of the information is varied by changing the variance of the distributions tones with high reliability are sampled from distributions with relatively small variance whereas tones with low reliability are sampled from distributions with relatively large variance results show that the observations are weighted more efficiently when the tones have equal rather than unequal reliability and when the most reliable tones have the greater intensity additional results show that the most intense tones often receive the greatest weight even when those tones have the least reliability

auditory intensity perception successive versus simultaneous across channel discriminations this study measures the ability of observers to compare the intensities of two stimuli occupying different frequency regions it includes three experiments each experiment having two conditions in one condition the two stimuli to be compared were presented simultaneously within each interval this condition has been called profile analysis in the other condition the two stimuli were presented successively within each interval because the overall level of the stimuli was randomized between intervals the observers were encouraged to compare the intensities of the two stimuli within each observation interval rather than between intervals the stimuli were two simple tones in experiment 1 and two tonal complexes in both experiments 2 and 3 the stimuli used in experiments 2 and 3 differed in frequency the results show that simultaneous comparisons are superior to successive comparisons for simple tones the difference in threshold is about 8 db for complexes with 10 to 11 components the difference

a determinant based criterion for working correlation structure selection in generalized estimating equations in generalized estimating equations gee the correlation between the repeated observations on a subject is specified with a working correlation matrix correct specification of the working correlation structure ensures efficient estimators of the regression coefficients among the criteria used in practice for selecting working correlation structure rotnitzky jewell quasi information criterion qic and correlation information criterion cic are based on the fact that if the assumed working correlation structure is correct then the model based naive and the sandwich robust covariance estimators of the regression coefficient estimators should be close to each other the sandwich covariance estimator used in defining the rotnitzky jewell qic and cic criteria is biased downward and has a larger variability than the corresponding model based covariance estimator motivated by this fact a new criterion is proposed in this paper based on the bias corrected sandwich covariance estimator for selecting an appropriate working correlation structure in gee a comparison of the proposed and the competing criteria is shown using simulation studies with correlated binary responses the results revealed that the proposed criterion generally performs better than the competing criteria an example of selecting the appropriate working correlation structure has also been shown using the data from madras schizophrenia study

individual differences in the improvement in spectral shape discrimination due to increasing number of nonsignal tones the effect of the number of nonsignal tones on the just discriminable difference in spectral shape was evaluated for 12 naive subjects the signal was an intensity increment to the center tone of a multitone complex the tones were spaced at equal frequency ratios and except for the signal increment were equal in level the number of nonsignal tones ranged from 2 to 20 consistent with previous studies using equally spaced components group mean thresholds improved monotonically with increasing number of tones group mean thresholds improved about 8 db over the range of reference spectra employed large differences were found across subjects in overall performance and in the magnitude of the improvement with increasing number of nonsignal tones the greatest intersubject variability was observed for the stimuli composed of the fewest components it was concluded that the differences reported in the literature concerning the presence and magnitude of the improvement are due both to differences in the pr

effects of a limited class of nonlinearities on estimates of relative weights perturbation analyses have been applied in recent years to determine the relative contribution of individual stimulus components in detection and discrimination tasks responses to stimulus samples are compared to stimulus parameters to determine the details of the decision rule often a linear model is assumed and it is of interest to determine the relative contribution of different stimulus elements to the decision here biases in estimated relative weights are considered for the case where the decision variable is given by d ixin k m and the stimulus components the xi are normally distributed of equal variance and mutually independent the i are the true combination weights and n k and m are positive reals the method used to estimate relative weights is the correlation coefficient between the xi and the observer s responses estimates of relative i do not depend on m but may depend on the mean values of the xi and the values of n and k a dependence on the variance i2 holds even fo

the analysis of binary longitudinal data with time dependent covariates we consider longitudinal studies with binary outcomes that are measured repeatedly on subjects over time the goal of our analysis was to fit a logistic model that relates the expected value of the outcomes with explanatory variables that are measured on each subject however additional care must be taken to adjust for the association between the repeated measurements on each subject we propose a new maximum likelihood method for covariates that may be fixed or time varying we also implement and make comparisons with two other approaches generalized estimating equations which may be more robust to misspecification of the true correlation structure and alternating logistic regression which models association via odds ratios that are subject to less restrictive constraints than are correlations the proposed estimation procedure will yield consistent and asymptotically normal estimates of the regression and correlation parameters if the correlation on consecutive measurements on a subject is correctly specified simulations demonstrate that our approach can yield improved efficiency in estimation of the regression parameter for equally spaced and complete data the gains in efficiency were greatest for the parameter associated with a time by group interaction term and for stronger values of the correlation for unequally spaced data and with dropout according to a missing at random mechanism mark1ml with correctly specified consecutive correlations yielded substantial improvements in terms of both bias and efficiency we present an analysis to demonstrate application of the methods we consider we also offer an r function for easy implementation of our approach copyright 2012 john wiley sons ltd

auditory profile analysis frequency phase and weber s law this paper reports three separate experiments on different aspects of performance in auditory profile analysis the first experiment deals with the effects of the frequency and position of an increment in a single component of a multitonal complex the general results indicate that detection of the signal is easier for components in the mid frequency range around 1000 hz independent of signal position within the complex the second experiment investigates the effects of relative phase of the individual components of the complex regardless of the number of components our results indicate that phase has very little effect even when different phases are selected for each presentation the third experiment compares the detection of an increment in intensity of a single component the traditional weber fraction experiment and conditions where additional components are present a profile experiment the detection of the increment is measured as a function of the level of the standard the single tone condition shows the usual near miss to weber s law whereas the multitone condition does not in addition threshold for the increment is better for the multitone condition than for the single tone condition for levels of the standard up to 70 db spl this last result is investigated for ten observers five of whom were experienced in profile tasks and five of whom were not using a low level standard the five experienced observers replicate the results described above the inexperienced observers show the opposite result on average they are better able to detect the increment in the single component condition

a note on implementation of decaying product correlation structures for quasi least squares this note implements an unstructured decaying product matrix via the quasi least squares approach for estimation of the correlation parameters in the framework of generalized estimating equations the structure we consider is fairly general without requiring the large number of parameters that are involved in a fully unstructured matrix it is straightforward to show that the quasi least squares estimators of the correlation parameters yield feasible values for the unstructured decaying product structure furthermore subject to conditions that are easily checked the quasi least squares estimators are valid for longitudinal bernoulli data we demonstrate implementation of the structure in a longitudinal clinical trial with both a continuous and binary outcome variable

evaluation of simple models of auditory profile analysis using random reference spectra this article describes further study of the finding reported by green et al j acoust soc am 73 639 643 1983 and others that in certain conditions the threshold of detectability for an intensity increment to the center tone of a multitone reference spectrum decreased as the number of nonsignal tones increased that result was considered remarkable since critical band theory would predict that these nonsignal tones spaced outside the critical band containing the signal would have no effect on or at most slightly decrease within band detectability and certainly could not account for the result of improved detectability found in the study cited above recently henn and turner j acoust soc am 88 126 131 1990 were unable to replicate the result described above concluding that the phenomenon exists only in limited conditions and that it is highly individual in nature further they speculated that the most likely reason for the discrepancy between their study and previous s

on the accuracy of efficiency of estimating equation approach summary liang and zeger 1986 biometrika73 13 22 introduced a generalized estimating equation gee approach based on a working correlation matrix to obtain efficient estimators of regression parameters in the class of generalized linear models for repeated measures data as demonstrated by crowder 1995 biometrika82 407 410 because of uncertainty of the definition of the working correlation matrix the liang zeger approach may in some cases lead to a complete breakdown of the estimation of the regression parameters after taking this comment of crowder into account recently sutradhar and das 1999 biometrika86 459 465 examined the loss of efficiency of the regression estimators due to misspecification of the correlation structures but their study was confined to the regression estimation with cluster level covariates as in the original paper of liang and zeger in this paper we study this efficiency loss problem for the generalized regression models with within cluster covariates by utilizing the approach of sutsadhar and das 1999

spectral weights for sample discrimination as a function of overall level doherty and lutfi 1996 spectral weights for overall level discrimination in listeners with sensorineural hearing loss j acoust soc am 99 1053 1058 examined the weights assigned to individual components of a six tone complex during a sample discrimination task and reported that hearing impaired subjects gave the most weight to components in the region of their high frequency hearing loss in contrast weighting patterns varied for normal hearing subjects in the current study the same six tone complex comprised of the octave frequencies from 0 25 to 8 khz was presented to three subjects with normal hearing in high pass noise in low pass noise and in quiet at two overall levels consistent with doherty and lutfi subjects assigned more weight to the 4 khz component in the high pass noise condition but roughly equal weight to all components in the lower level quiet condition weights in the low pass noise and higher level quiet conditions however were similar to those in the high pass no

spectral peak selection in spectral shape discrimination by normal hearing and hearing impaired listeners spectral shape discrimination thresholds were measured in the presence and absence of noise to determine whether normal hearing and hearing impaired listeners rely primarily on spectral peaks in the excitation pattern when discriminating between stimuli with different spectral shapes standard stimuli were the sum of 2 4 6 8 10 20 or 30 equal amplitude tones with frequencies fixed between 200 and 4000hz signal stimuli were generated by increasing and decreasing the levels of every other standard component the function relating the spectral shape discrimination threshold to the number of components n showed an initial decrease in threshold with increasing n and then an increase in threshold when the number of components reached 10 and 6 for normal hearing and hearing impaired listeners respectively the presence of a 50 db spl hz noise led to a 1 7db increase in threshold for normal hearing listeners and a 3 5db increase for hearing impaired listeners multichannel modeling and the relatively s

analysis of repeated bouts of measurements in the framework of generalized estimating equations we consider a longitudinal study of interstitial cystitis ic in women in which the time between bouts of repeated measurements is large relative to the within bout separation in time our outcome of interest is the number of nocturnal voids that we model via quasi least squares qls in the framework of generalized estimating equations gee to account for potential intra subject correlation we directly apply a banded toeplitz correlation structure that previously was only implemented in an ad hoc approach using gee we describe this structure its appropriateness for data from the ic study and the results of our analysis we then demonstrate that correct specification of the underlying correlation structure versus incorrectly applying a simpler structure can prevent substantial losses in efficiency in estimation of the regression parameter these comparisons involve the limiting values of the estimates of the correlation parameters which are not consistent for the misspecification scenarios considered here we therefore obtain the limiting values of the qls estimates when the structure is incorrectly specified

efficiency of generalized estimating equations for binary responses summary using standard correlation bounds we show that in generalized estimation equations gees the so called working correlation matrix r for analysing binary data cannot in general be the true correlation matrix of the data methods for estimating the correlation param eter in current gee software for binary responses disregard these bounds to show that the gee applied on binary data has high efficiency we use a multivariate binary model so that the covariance matrix from estimating equation theory can be compared with the inverse fisher information matrix but r should be viewed as the weight matrix and it should not be confused with the correlation matrix of the binary responses we also do a comparison with more general weighted estimating equations by using a matrix cauchy schwarz inequality our analysis leads to simple rules for the choice of in an exchangeable or autoregressive ar 1 weight matrix r based on the strength of dependence between the binary variables an example is given to illustrate the assessment of dependence and choice of

auditory profile analysis of irregular sound spectra the discrimination of changes in the shapes of sound spectra is reported the change was always an intensity increment to the 948 hz component of a multitone complex first the ability of naive listeners to learn to discriminate a change in a regular background or reference spectrum equal level tones equally spaced in logarithmic frequency was measured as a function of the number of trials on the average threshold improved about 10 db over 3000 trials with about 50 of the decrease in threshold occurring during the first 750 trials in a subsequent series of experiments the overall pattern of spectral shape of the background was varied randomly two kinds of perturbations in spectral shape were employed 1 randomly choosing the frequencies of the reference spectra and 2 randomly choosing the amplitudes of the components of the reference spectra the experimental manipulations involved fixing the random spectra across a block of trials varying the reference spectra from interval to interval of each trial and providing extensive practice in discriminating specific randomly perturbed reference spectra the results of the spectrum learning and random perturbation experiments provide insight into the roles of critical band filtering sensory variability and short term and long term memory representations in auditory profile analysis further the appropriateness of the generalization of a simple energy detection model is discussed

relative weights for three different psychophysical tasks relative weights for two profile analysis and one detection task were estimated for the profile analysis bump task the standard was the sum of n equal amplitude sinusoidal components ranging in frequency from 200 to 5000 hz the signal for this task was an increment in level to the 1000 hz component of the standard the number of components n ranged from 4 to 50 for the profile analysis down up task the standard was composed of n equal amplitude tones ranging in frequency from 200 to 5000 hz the signal to be detected led to a spectrum that varied down up down up the detection task used the same standard as the profile analysis down up task but the signal to be detected was an added 1000 hz tone comparisons of the relative weights revealed that profile analysis bump and the detection of a tone added to a notched masker rely on similar processing strategies by contrast it was apparent that auditory processing in the profile analysis down up task depended on a different strategy than the other two tasks finally rough estimates of the auditory filter bandwidths suggest invariance with regard to task work supported by nih

object localization using color texture and shape abstract we address the problem of localizing objects using color texture and shape given a handrawn sketch for querying an object shape and its color and texture the proposed algorithm automatically searches the image database for objects which meet the query attributes the database images do not need to be presegmented or annotated the proposed algorithm operates in two stages in the first stage we use local texture and color features to find a small number of candidate images in the database and identify regions in the candidate images which share similar texture and color as the query to speed up the processing the texture and color features are directly extracted from the discrete cosine transform dct compressed domain in the second stage we use a deformable template matching method to match the query shape to the image edges at the locations which possess the desired texture and color attributes this algorithm is different from other content based image retrieval algorithms in that i no presegmentation of the database images is needed and ii the color and texture features are directly extracted from the compressed images experimental results demonstrate performance of the algorithm and show that substantial computational savings can be achieved by utilizing multiple image cues

frequency correlation functions for the detection of a tone added to modulated noise maskers psychophysical experiments using reproducible stimuli were completed for the detection of a 1000 hz tone added to a masker the noise masker was either sinusoidally amplitude modulated or not and masker bandwidths of 100 300 and 900 hz were tested the masker was centered at 1000 hz and the rate of amplitude modulation when present was 29 hz on average comodulation masking release values of 10 and 16 db were obtained for the 300 and 900 hz wide maskers respectively no release from masking was obtained for the 100 hz wide maskers data analysis consisted of computing the correlation coefficient between the level of each spectral component of each stimulus token and the observers responses to that token the resulting correlation functions estimate the relative contribution or weight of different frequency regions to the observers responses while the correlation functions for the modulated and unmodulated maskers share some features differences in both the pattern and quality of fit are apparent for wideband maskers for two of the observers however restricting the region of comparison to the region surrounding the signal frequency led to increased similarity of the correlation functions

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

the number of components in profile analysis tasks the central issue of this paper is how detection of a change in spectral shape depends on the number of components m that define the spectrum first a channel theory is reviewed and the predictions relating the detectability of such a change as a function of the number of components are derived second the existing literature is reviewed most of it concerns the detection of an increment in a single tone of an m component equal amplitude complex the data are close 2 db to the predictions of the theory which suggests that there is a relatively small change in threshold as the number of components increases the consistency of the data is also discussed and hypotheses for discrepancies are presented finally the results of an experiment measuring the detectability of a special spectral shape change is explored in this case all the changes are equal in size but some are opposite in sign so that the summed change is zero the results using this balanced spectral change are also consistent with the predictions of the theory and show that for this special kind of spectral change thresholds improve by nearly 7 db as m increases from 4 to 24 components

sample size for a two group comparison of repeated binary measurements using gee controlled clinical trials often randomize subjects to two treatment groups and repeatedly evaluate them at baseline and intervals across a treatment period of fixed duration a popular primary objective in these trials is to compare the change rates in the repeated measurements between treatment groups repeated measurements usually involve missing data and a serial correlation within each subject the generalized estimating equation gee method has been widely used to fit the time trend in repeated measurements because of its robustness to random missing and misspecification of the true correlation structure in this paper we propose a closed form sample size formula for comparing the change rates of binary repeated measurements using gee for a two group comparison the sample size formula is derived incorporating missing patterns such as independent missing and monotone missing and correlation structures such as ar 1 model we also propose an algorithm to generate correlated binary data with arbitrary marginal means and a markov dependency and use it in simulation studies copyright 2005 john wiley sons ltd

spectral weighting strategies for hearing impaired listeners measured using a correlational method spectral weighting strategies using a correlational method r a lutfi j acoust soc am 97 1333 1334 1995 v m richards and s zhu j acoust soc am 95 423 424 1994 were measured in ten listeners with sensorineural hearing loss on a sentence recognition task sentences and a spectrally matched noise were filtered into five separate adjacent spectral bands and presented to listeners at various signal to noise ratios snrs five point biserial correlations were computed between the listeners response correct or incorrect on the task and the snr in each band the stronger the correlation between performance and snr the greater that given band was weighted by the listener listeners were tested with and without hearing aids on all listeners were experienced hearing aid users results indicated that the highest spectral band 2800 11000hz received the greatest weight in both listening conditions however the weight on the highest spectral band was less when listeners performed the tas

sample discrimination of frequency by hearing impaired and normal hearing listeners in a multiple observation sample discrimination experiment normal hearing nh and hearing impaired hi listeners heard two multitone complexes each consisting of six simultaneous tones with nominal frequencies spaced evenly on an erbn logarithmic scale between 257 and 6930hz on every trial the frequency of each tone was sampled from a normal distribution centered near its nominal frequency in one interval of a 2ifc task all tones were sampled from distributions lower in mean frequency and in the other interval from distributions higher in mean frequency listeners had to identify the latter interval decision weights were obtained from multiple regression analysis of the between interval frequency differences for each tone and listeners responses frequency difference limens an index of sensorineural resolution and decision weights for each tone were used to predict the sensitivity of different decision theoretic models results indicate that low frequency tones were given much greater perceptu

the design of simulation studies in medical statistics by andrea burton douglas g altman patrick royston and roger l holder statistics in medicine 2006 25 4279 4292

level discrimination of single tones in a multitone complex by normal hearing and hearing impaired listeners a conditional on a single stimulus coss analysis procedure j acoust soc am 86 1743 1746 1989 was used to estimate how well normal hearing and hearing impaired listeners selectively attend to individual spectral components of a broadband signal in a level discrimination task on each trial two multitone complexes consisting of six octave frequencies from 250 to 8000 hz were presented to listeners the levels of the individual tones were chosen independently and at random on each presentation the target tone was selected within a block of trials as the 250 1000 or 4000 hz component on each trial listeners were asked to indicate which of the two complex sounds contained the higher level target as a group normal hearing listeners exhibited greater selectivity than hearing impaired listeners to the 250 hz target while hearing impaired listeners showed greater selectivity than normal hearing listeners to the 4000 hz target which is in the region of their hearing loss both groups of listeners displayed large variability in their ability to selectively weight the 1000 hz target trial by trial analysis showed a decrease in weighting efficiency with increasing frequency for normal hearing listeners but a relatively constant weighting efficiency across frequency for hearing impaired listeners interestingly hearing impaired listeners selectively weighted the 4000 hz target which was in the region of their hearing loss more efficiently than did the normal hearing listeners

spectral weights in profile listening the coss analysis suggested by berg b g berg j acoust soc am 86 1743 1746 1989 is applied to a profile listening task the listener s task is to detect an increment in the level of the middle component of an n component spectrum the overall level of the components is randomly selected from a 20 db range on each presentation thus the detection task is essentially one of detecting a change in spectral shape to implement the coss analysis a small perturbation in level is added to each component of the complex coss functions are generated from these perturbations and the spectral weight that the listener assigns to each component is estimated data are reported for n 3 5 and 11 components and for perturbations with standard deviations of 0 5 1 and 2 db the estimated weights are similar to those derived for an optimum detector namely the level at the signal component is compared with the average level of the nonsignal components this result supports the view that profile analysis invol

individualized estimation of the speech intelligibility index for short sentences test retest reliability the speech intelligibility index sii model was modified to allow individualized parameters these parameters included the relative weights of speech cues in five octave frequency bands ranging from 0 25 to 4 khz i e the band importance function and the transfer function that allows the sii to generate predictions on speech recognition scores a bayesian adaptive procedure the quick band importance function qbif procedure was utilized to enable efficient estimation of the sii parameters from individual listeners in two experiments the sii parameters were estimated for 30 normal hearing adults using institute of electrical and electronics engineers ieee sentences at speech levels of 55 65 and 75 db sound pressure level in experiment i and for 15 hearing impaired hi adult listeners using amplified ieee or azbio sentences in experiment ii in both experiments even without prior training the estimated model parameters showed satisfactory reliability between two runs of the qbif procedure at least one week apart for the hi listeners inter listener variability in most estimated sii parameters was larger than intra listener variability of the qbif procedure

decision strategies of hearing impaired listeners in spectral shape discrimination the ability to discriminate between sounds with different spectral shapes was evaluated for normal hearing and hearing impaired listeners listeners detected a 920 hz tone added in phase to a single component of a standard consisting of the sum of five tones spaced equally on a logarithmic frequency scale ranging from 200 to 4200 hz an overall level randomization of 10 db was either present or absent in one subset of conditions the no perturbation conditions the standard stimulus was the sum of equal amplitude tones in the perturbation conditions the amplitudes of the components within a stimulus were randomly altered on every presentation for both perturbation and no perturbation conditions thresholds for the detection of the 920 hz tone were measured to compare sensitivity to changes in spectral shape between normal hearing and hearing impaired listeners to assess whether hearing impaired listeners relied on different regions of the spectrum to discriminate between sounds spectral weights were estimated from the perturbed standards by correlating the listener s responses with the level differences per component across two intervals of a two alternative forced choice task results showed that hearing impaired and normal hearing listeners had similar sensitivity to changes in spectral shape on average across frequency correlation functions also were similar for both groups of listeners suggesting that as long as all components are audible and well separated in frequency hearing impaired listeners can use information across frequency as well as normal hearing listeners analysis of the individual data revealed however that normal hearing listeners may be better able to adopt optimal weighting schemes this conclusion is only tentative as differences in internal noise may need to be considered to interpret the results obtained from weighting studies between normal hearing and hearing impaired listeners

correlation coefficients and correlation ratios as estimates of observer weights in multiple observation tasks advantages of correlational methods are described for estimating the relative reliance or weight observers give to different elements of a complex display when performing auditory or visual discriminations correlational methods differ from other such methods by providing a least squares estimate of weights rather than a maximum likelihood estimate based on a presumed model the main benefit is that these methods can be generally applied in cases where the statistical properties of elements are unknown where correlations exist between elements or where it is necessary to evaluate decision models that are inherently nonlinear

correlation structure and variable selection in generalized estimating equations via composite likelihood information criteria the method of generalized estimating equations gee is popular in the biostatistics literature for analyzing longitudinal binary and count data it assumes a generalized linear model for the outcome variable and a working correlation among repeated measurements in this paper we introduce a viable competitor the weighted scores method for generalized linear model margins we weight the univariate score equations using a working discretized multivariate normal model that is a proper multivariate model because the weighted scores method is a parametric method based on likelihood we propose composite likelihood information criteria as an intermediate step for model selection the same criteria can be used for both correlation structure and variable selection simulations studies and the application example show that our method outperforms other existing model selection methods in gee from the example it can be seen that our methods not only improve on gee in terms of interpretability and efficiency but also can change the inferential conclusions with respect to gee copyright 2016 john wiley sons ltd

sample size calculations for studies with correlated observations correlated data occur frequently in biomedical research examples include longitudinal studies family studies and ophthalmologic studies in this paper we present a method to compute sample sizes and statistical powers for studies involving correlated observations this is a multivariate extension of the work by self and mauritsen 1988 biometrics 44 79 86 who derived a sample size and power formula for generalized linear models based on the score statistic for correlated data we appeal to a statistic based on the generalized estimating equation method liang and zeger 1986 biometrika 73 13 22 we highlight the additional assumptions needed to deal with correlated data some special cases that are commonly seen in practice are discussed followed by simulation studies

analysis of serially correlated data using quasi least squares summary quasi least squares qls a marginal statistical approach via generalized estimating equations that is described in the balanced data setting by chaganty 1997 journal of statistical planning and inference 63 39 54 allows for application of a wide range of working correlation structures when analyzing serially correlated data we extend the application of qls to serially correlated unequally spaced and unbalanced data using three useful working correlation models the firstorder autoregressive ar 1 the markov and the generalized markov structure described by nuniez anton and woodworth 1994 biometrics 50 445 456 we compare qls and the original formulation of the generalized estimating equation approach gee for these structures demonstrating that i infeasibility of the gee correlation parameter estimates can be a problem ii it is difficult to obtain consistent moment estimates of the correlation parameters for the generalized markov structure and iii the use of qls can lead to reduced mean square error of the estimate of the regression parameter for small samples of moderately correlated data to choose between alternative correlation models we propose a criterion that is based on the principle of generalized least squares finally data for which the generalized markov structure is appropriate are analyzed to demonstrate the use of qls in selecting a suitable working correlation structure and identifying in this paper we apply a statistical method based on the generalized estimating equation approach of liang and zeger 1986 to the analysis of longitudinal data that may be difficult to analyze using other established methods we consider repeated measures data collected by taking measurements of an outcome variable and associated covariates on each of a group of independent subjects our primary data analysis goal is to identify important covariates and to explain their effect on the marginal mean of the outcome variable while also accounting for the correlation among observations on each subject accomplishing this research objective may be difficult due to certain conditions that are typical in longitudinal studies the timing and total number of measurements taken may vary from subject to subject so that the data may be unbalanced and unequally spaced the outcome variable may not be normally distributed the intrasubject correlation may be described using a time dependent pattern for example the correlation between two measurements may decrease as they become more

relative estimates of combination weights decision criteria and internal noise based on correlation coefficients a means by which relative combination weights may be determined is described for a signal detection model in which the decision variable is a weighted linear combination of several independent normally distributed random variables xi s the first theorem presents the correlation between the binary response variables signal versus no signal and the component xi the second theorem presents a parallel result for the case that additive internal noise is present thus in psychophysical experiments the relative combination weights may be obtained by correlating the observers responses and the input random variables third three numerical methods which allow the evaluation of the relative magnitude of the decision criterion and the variance of a hypothetical additive internal noise are considered

three dimensional structural texture modeling and segmentation the structural approach one of the various modeling techniques in texture analysis perceives texture as a region composed of detectable primitive elements tokens in this paper we extend this concept to three dimensional 3d image and develop a segmentation scheme based on clustering of 3d texture tokens 3d structural texture is composed of texture tokens which are modeled as tiny objects embedded inside image sequence texture tokens located spatially close to one another and having similar shape are grouped into homogenous texture volume some of the texture tokens may be in contact with one another to form clump like structures our approach first disconnects these clumps by a 3d clump decomposition process a 3d irregular pyramid construction process is then carried out on these isolated 3d tokens the process inputs a delaunay graph with each vertex representing the shape feature vector of a texture token and each edge representing the neighborhood relationship of two texture tokens through stepwise grouping of similar shape tokens a segmentation of the texture volume is obtained

a generalized estimating equations approach for spatially correlated binary data applications to the analysis of neuroimaging data this paper proposes a generalized estimating equations approach for the analysis of spatially correlated binary data when there are large numbers of spatially correlated observations on a moderate number of subjects this approach is useful when the scientific focus is on modeling the marginal mean structure proper modeling of the spatial correlation structure is shown to provide large efficiency gains along with precise standard error estimates for inference on mean structure parameters generalized estimating equations for estimating the parameters of both the mean and spatial correlation structure are proposed the use of semivariogram models for parameterizing the correlation structure is discussed and estimation of the sample semivariogram is proposed as a technique for choosing parametric models and starting values for generalized estimating equations estimation the methodology is illustrated with neuroimaging data collected as part of the national institute of neurological disorders and stroke ninds stroke data bank a simulation study demonstrates the importance of accurate modeling of the spatial correlation structure in data with large numbers of spatially correlated observations such as those found in neuroimaging studies

sensitivity to changes in overall level and spectral shape an evaluation of a channel model two experiments involving level and spectral shape discrimination which test an optimal channel model developed by durlach et al j acoust soc am 80 63 72 1986 are described the model specifies how the auditory system compares and or combines intensity information in different frequency channels in the first experiment psychometric functions were obtained for the discrimination of changes in level and discrimination of changes in spectral shape for an eight tone complex sound a variety of different base spectral shapes were tested in some conditions level randomization was introduced to reduce the reliability of across interval changes in level increasing the amount of level variation degraded performance for the level discrimination task but had no effect on the shape discrimination task in all conditions sensitivity to changes in spectral shape was superior to sensitivity to changes in level consequently two models of central noise are evaluated in an attempt to explain these results one in which central noise acts prior to the formation of the likelihood ratio and one in which central noise degrades the likelihood ratio the former model is more successful in accounting for the data in a second experiment the detectability of a level increment to one component of a multitone complex was measured the frequency content of the complex was varied by systematically removing six components from a 23 component complex thresholds were measured for increments at three different signal frequencies a common trend in the data was that when there was a spectral gap directly above the signal frequency thresholds were lowest this result differs from the predictions of a simple channel model and contrasts with results presented by green and berg q j exp psychol 43a 449 458 1991

molecular analysis of the effect of relative tone level on multitone pattern discrimination molecular psychophysics attempts to model the observer s response to stimuli as they vary from trial to trial the approach has gained popularity in multitone pattern discrimination studies as a means of estimating the relative reliance or decision weight listeners give to different tones in the pattern various factors affecting decision weights have been examined but one largely ignored is the relative level of tones in the pattern in the present study listeners detected a level increment in a sequence of 5 100 ms 2 0 khz tone bursts alternating in level between 40 and 80db spl the level increment was made largest on the 40 db tones yet despite this all four highly practiced listeners gave near exclusive weight to the 80 db tones the effect was the same when the tones were replaced by bursts of broadband gaussian noise alternating in level it was reduced only when the level differences were made 10db and it was entirely reversed only when the low level tones alternated with louder bursts of ga

improving the correlation structure selection approach for generalized estimating equations and balanced longitudinal data generalized estimating equations are commonly used to analyze correlated data choosing an appropriate working correlation structure for the data is important as the efficiency of generalized estimating equations depends on how closely this structure approximates the true structure therefore most studies have proposed multiple criteria to select the working correlation structure although some of these criteria have neither been compared nor extensively studied to ease the correlation selection process we propose a criterion that utilizes the trace of the empirical covariance matrix furthermore use of the unstructured working correlation can potentially improve estimation precision and therefore should be considered when data arise from a balanced longitudinal study however most previous studies have not allowed the unstructured working correlation to be selected as it estimates more nuisance correlation parameters than other structures such as ar 1 or exchangeable therefore we propose appropriate penalties for the selection criteria that can be imposed upon the unstructured working correlation via simulation in multiple scenarios and in application to a longitudinal study we show that the trace of the empirical covariance matrix works very well relative to existing criteria we further show that allowing criteria to select the unstructured working correlation when utilizing the penalties can substantially improve parameter estimation copyright 2014 john wiley sons ltd

successive versus simultaneous comparison in auditory intensity discrimination the ability to discriminate between two brief sounds having identical frequency components but differing in the intensity of one or more of the components is studied the stimulus manipulations include randomizing the overall intensity of the sounds varying the number and spacing of the components and varying the interval of time between the sounds the results from the experiment in which interstimulus interval is manipulated clearly support a profile analysis mechanism that computes two rough spectral analyses stores a classification of these spectra in memory and compares the two stores this profile mechanism involves a simultaneous comparison of different components of the complex some remote from the signal frequency rather than a successive comparison of the difference in intensity at the signal frequency the simultaneous comparison process is more sensitive when the profile is composed of many components spaced over a wide frequency range

entropy based texture analysis in the spatial frequency domain an approach which uses regional entropy measures in the spatial frequency domain for texture discrimination is presented the measures provide texture discriminating information independent of that contained in the usual summed energy within based frequency domain features performance of the entropy features as measured by a between to within class scatter criterion is comparable to that of traditional frequency domain features and gray level co occurrence contrast features a method of frequency scaling is introduced to enable the comparison of texture samples of different subimage size the resulting regional entropy measures are subimage size invariant subject to certain constraints which arise from properties of the discrete fourier transform

spectral weighting strategies for sentences measured by a correlational method listeners ability to understand speech in adverse listening conditions is partially due to the redundant nature of speech natural redundancies are often lost or altered when speech is filtered such as done in ai sii experiments it is important to study how listeners recognize speech when the speech signal is unfiltered and the entire broadband spectrum is present a correlational method r a lutfi j acoust soc am 97 1333 1334 1995 v m richards and s zhu j acoust soc am 95 423 424 1994 has been used to determine how listeners use spectral cues to perceive nonsense syllables when the full speech spectrum is present k a doherty and c w turner j acoust soc am 100 3769 3773 1996 c w turner et al j acoust soc am 104 1580 1585 1998 the experiments in this study measured spectral weighting strategies for more naturally occurring speech stimuli specifically sentences using a correlational method for normal hearing listeners results indicate that listeners placed the greatest weight on spectral information within bands 2 and 5 562 1113 and 2807 11 000 hz respectively spectral weighting strategies for sentences were also compared to weighting strategies for nonsense syllables measured in a previous study c w turner et al 1998 spectral weighting strategies for sentences were different from those reported for nonsense syllables

a new image distortion measure based on a data driven multisensor organization this paper describes a visual model that gives a perceptual distortion measure between an input image and that of reference based on a human image representational model we study an approach in which once a few active recognizers tuned to significant orientation and spatial frequency components of the reference spectrum are obtained any input image to be compared with the reference one is passed through an operator designated to compare its excitation levels given by the active recognizers to the corresponding excitation levels for the reference image hence the distortion between a pair of complex images is measured as the weighted sum of the distortion in each filter of a bank of strongly responding recognizers each tuned to a certain 2d spatial frequency data in the reference picture with the weighting of each filter modulating its amplitude response

on the use of a working correlation matrix in using generalised linear models for repeated measures summary in a seminal paper liang zeger 1986 extended the use of generalised linear models to repeated measures data they based the analysis on specifications for the means and variances of the observations as usual for generalised linear models but showed how specifications for the correlations between measurements made on the same unit could be avoided by using a working correlation matrix in some cases the parameters involved in this matrix are subject to an uncertainty of definition which can lead to a breakdown of the asymptotic properties of the estimators

the selection of natural scales in 2d images using adaptive gabor filtering this paper analyzes how the natural scales of the shapes in 2d images can be extracted spatial information is analyzed by multiple units sensitive to both spatial and spatial frequency variables scale estimates of the relevant shapes are constructed only from strongly responding detectors the meaningful structures in the response of a detector computed through 2d gabor filtering are at their natural level of resolution relatively sharp and have well defined boundaries a natural scale is so defined as a level producing local minimum of a function that returns the relative sharpness of the detector response filtered over a range of scales in a second stage to improve a first crude estimate of the local scale the criterion is also rewritten to directly select scales at locations of significant features of each activated detector

a composite randomization procedure for measuring spectral shape discrimination in studies of auditory profile analysis d m green profile analysis auditory intensity discrimination oxford u p new york 1988 the sounds are presented at random levels to discourage the listener from basing the discrimination on a difference in absolute level rather than on a difference in the shape of the spectrum a difference in absolute level however can still provide an effective discrimination cue if the difference is comparable to the range of randomization using enormous ranges of random levels is not desirable because it is distracting to normal listeners and may exceed the dynamic range of hearing for listeners with hearing loss this article describes a new experimental procedure which permits the experimenter to greatly reduce the range of level randomization in roving level tasks

minimum spectral contrast for vowel identification by normal hearing and hearing impaired listeners to determine the minimum difference in amplitude between spectral peaks and troughs sufficient for vowel identification by normal hearing and hearing impaired listeners four vowel like complex sounds were created by summing the first 30 harmonics of a 100 hz tone the amplitudes of all harmonics were equal except for two consecutive harmonics located at each of three formant locations the amplitudes of these harmonics were equal and ranged from 1 8 db more than the remaining components normal hearing listeners achieved greater than 75 accuracy when peak to trough differences were 1 2 db normal hearing listeners who were tested in a noise background sufficient to raise their thresholds to the level of a flat moderate hearing loss needed a 4 db difference for identification listeners with a moderate flat hearing loss required a 6 to 7 db difference for identification the results suggest for normal hearing listeners that the peak to trough amplitude difference required for identification of this set of vowels is very near the threshold for detection of a change in the amplitude spectrum of a complex signal hearing impaired listeners may have difficulty using closely spaced formants for vowel identification due to abnormal smoothing of the internal representation of the spectrum by broadened auditory filters

unbiased estimating equations from working correlation models for irregularly timed repeated measures the method of generalized estimating equations gees has been criticized recently for a failure to protect against misspecification of working correlation models which in some cases leads to loss of efficiency or infeasibility of solutions however the feasibility and efficiency of gee methods can be enhanced considerably by using flexible families of working correlation models we propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance gee the supplementary estimating equations are obtained by differentiation of the cholesky decomposition of the working correlation or as score equations for decoupled gaussian pseudolikelihood the estimating equations are solved with computational effort equivalent to that required for a first order gee full details and analytic expressions are developed for a generalized markovian model that was evaluated through simulation large sample sandwich standard errors for working correlation parameter estimates are derived and shown to have good performance the proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children

a family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations summary we introduce a family of multivariate binary distributions with certain conditional linear property this family is particularly useful for efficient and easy simulation of correlated binary variables with a given marginal mean vector and correlation matrix

decision rules of listeners in spectral shape discrimination with or without signal frequency uncertainty a correlation technique was used to assess the decision rules of three listeners in two cases of spectral shape discrimination tasks in one case the signal frequency was fixed and in the other it was randomly varied within each block of trials in order to estimate the decision rule of the listeners the experimenter superimposed random level perturbations on each frequency component upon each stimulus presentation over many trials correlation coefficients were computed between the random perturbations and the binary responses of the listeners and were expressed as a function of signal level for both the fixed and random signal cases the measured correlation functions were in reasonably good agreement with those predicted based on the likelihood ratio decision rules thus the listeners appeared to use information nearly optimally in discriminating spectral shapes this investigation demonstrated that the correlation technique can be used to reveal the decision rules for cases where the decision statistics are nonlinear functions of the observations

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

a comparison of several approaches for choosing between working correlation structures in generalized estimating equation analysis of longitudinal binary data the method of generalized estimating equations gee models the association between the repeated observations on a subject with a patterned correlation matrix correct specification of the underlying structure is a potentially beneficial goal in terms of improving efficiency and enhancing scientific understanding we consider two sets of criteria that have previously been suggested respectively for selecting an appropriate working correlation structure and for ruling out a particular structure s in the gee analysis of longitudinal studies with binary outcomes the first selection criterion chooses the structure for which the model based and the sandwich based estimator of the covariance matrix of the regression parameter estimator are closest while the second selection criterion chooses the structure that minimizes the weighted error sum of squares the rule out criterion deselects structures for which the estimated correlation parameter violates standard constraints for binary data that depend on the marginal means in addition we remove structures from consideration if their estimated parameter values yield an estimated correlation structure that is not positive definite we investigate the performance of the two sets of criteria using both simulated and real data in the context of a longitudinal trial that compares two treatments for major depressive episode practical recommendations are also given on using these criteria to aid in the efficient selection of a working correlation structure in gee analysis of longitudinal binary data