the heteroscedastic graded response model with a skewed latent trait testing statistical and substantive hypotheses related to skewed item category functions the graded response model grm samejima estimation of ability using a response pattern of graded scores psychometric monograph no 17 richmond va the psychometric society 1969 can be derived by assuming a linear regression of a continuous variable z on the trait to underlie the ordinal item scores takane de leeuw in psychometrika 52 393 408 1987 traditionally a normal distribution is specified for z implying homoscedastic error variances and a normally distributed in this paper we present the heteroscedastic grm with skewed latent trait which extends the traditional grm by incorporation of heteroscedastic error variances and a skew normal latent trait an appealing property of the extended grm is that it includes the traditional grm as a special case this enables specific tests on the normality assumption of z we show how violations of normality in z can lead to asymmetrical category response functions the ability to test this normality assumption is beneficial from both a statistical and substantive perspective in a simulation study we show the viability of the model and investigate the specificity of the effects we apply the model to a dataset on affect and a dataset on alexithymia

random walk theory of jamming in a cellular automaton model for traffic flow abstract the jamming behavior of a single lane traffic model based on a cellular automaton approach is studied our investigations concentrate on the so called vdr model which is a simple generalization of the well known nagel schreckenberg model in the vdr model one finds a separation between a free flow phase and jammed vehicles this phase separation allows to use random walk like arguments to predict the resolving probabilities and lifetimes of jam clusters or disturbances these predictions are in good agreement with the results of computer simulations and even become exact for a special case of the model our findings allow a deeper insight into the dynamics of wide jams occuring in the model

finite size effects in a field theoretic model with long range exchange interaction we present a systematic approach to the calculation of finite size fs effects for ano n field theoretic model with both short range sr and long range lr exchange interactions the lr exchange interaction decays at large distances as 1 rd 2 2 0 0 renormalization group calculations ind du e are performed for a system with a fully finite block geometry under periodic boundary conditions we calculate the fs shift of the critical temperature and the fs renormalized coupling constant of the model to one loop order the universal scaling variable is obtained and the fs scaling hypothesis is verified

first order transitions in spherical models finite size scaling finite size behavior near the first order phase boundary of ferromagnetic spherical models is investigated for block and cylinder shaped systems ind dimensions the bulk thermodynamic singularities are rounded and asymptotically for large size obey appropriate scaling laws both short range interactions and long range couplings decaying like 1 rd with 0 are analyzed the short range results agree precisely with a recently developed scaling theory foro n symmetric systems in the limitn more generally the scaling functions are universal depending only on explicit aspects of the shape and interactions enter only in the spin wave or goldstone mode contributions which appear technically as corrections to scaling an appendix analyzes the truncation error in the approximation by many fold sums of multivariate integrals with integrands diverging like jaj j2 as 0

finite size scaling investigations in the quantum varphi4 model with long range interaction in this paper we study in detail the critical behaviour of the n quantum 4 model with long range interaction decaying with distances r by a power law as r d in the large n limit the zero temperature critical behaviour is discussed its alteration by finite temperature and or finite sizes in the space is studied the scaling behaviours are studied in different regimes depending upon whether the finite temperature or the finite sizes of the system lead a number of results for the correlation length critical amplitudes and the finite size shift for different dimensionalities between the lower d 3 2 critical dimensions are calculated

on anomalous diffusion and the fractional generalized langevin equation for a harmonic oscillator the fractional generalized langevin equation fgle is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two parameter mittag leffler noise the solution of this fgle is discussed by means of the laplace transform methodology and the kernels are presented in terms of the three parameter mittag leffler functions recent results associated with a generalized langevin equation are recovered

exact steady states of disordered hopping particle models with parallel and ordered sequential dynamics a one dimensional driven lattice gas with disorder in the particle hopping probabilities is considered it has previously been shown that in the version of the model with random sequential updating a phase transition occurs from a low density inhomogeneous phase to a high density congested phase here the steady states for both parallel fully synchronous updating and ordered sequential updating are solved exactly the phase transition is shown to persist in both cases with the critical densities being higher than that for random sequential dynamics the steady state velocities are related to the fugacity of a bose system suggesting a principle of minimization of velocity a generalization of the dynamics to the case where the hopping probabilities depend on the number of empty sites in front of the particles is also solved exactly in the case of parallel updating the models have natural interpretations as simplistic descriptions of traffic flow the relation to more sophisticated traffic flow models is discussed

combination of improved multibondic method and the wang landau method we propose a method for monte carlo simulation of statistical physical models with discretized energy the method is based on several ideas including the cluster algorithm the multicanonical monte carlo method and its acceleration proposed recently by wang and landau as in the multibondic ensemble method proposed by janke and kappler the present algorithm performs a random walk in the space of the bond population to yield the state density as a function of the bond number a test on the ising model shows that the number of monte carlo sweeps required of the present method for obtaining the density of state with a given accuracy is proportional to the system size whereas it is proportional to the system size squared for other conventional methods in addition the method shows a better performance than the original wang landau method in measurement of physical quantities

first order phase transitions of the potts model in fractal dimensions abstract the phase diagram of the q state potts model in fractal dimensions is studied with the help of wang landau monte carlo simulations on sierpinski and menger fractal structures a particular attention is paid to first order transitions just above the border separating the second order phase transition regime from the first order one although the translation invariance is strongly broken in deterministic fractals evidence is given that such a deviation from the translational symmetry is not able to induce second order transitions for large values of q when the dimension lies between 1 9746 and 3 moreover the occurrence of second order transitions for very large values of q in the case of hierarchically weakly connected systems that is when the fractal dimension is significantly smaller than 2 is pointed out at last the evolution of first order physical averages such as the latent heats and the interfacial free energies with the space dimensionality and the number of spin states is discussed

asymmetric fluid criticality ii finite size scaling for simulations the vapor liquid critical behavior of intrinsically asymmetric fluids is studied in finite systems of linear dimensions l focusing on periodic boundary conditions as appropriate for simulations the recently propounded complete thermodynamic stackrel ensuremath rightarrow l ensuremath infty scaling theory incorporating pressure mixing in the scaling fields as well as corrections to scaling phys rev e 67 061506 2003 is extended to finite l initially in a grand canonical representation the theory allows for a yang yang anomaly in which when stackrel ensuremath rightarrow l ensuremath infty the second temperature derivative d 2 ensuremath mu ensuremath sigma dt 2 of the chemical potential along the phase boundary ensuremath mu ensuremath sigma t diverges when stackrel ensuremath rightarrow t t mathrm c ensuremath the finite size behavior of various special critical loci in the temperature density or t ensuremath rho plane in particular the k inflection susceptibility loci and the q maximal loci derived from q l t ensuremath rho l ensuremath equiv m 2 l 2 m 4 l where m ensuremath equiv ensuremath rho ensuremath ensuremath rho l is carefully elucidated and shown to be of value in estimating t mathrm c and ensuremath rho mathrm c concrete illustrations are presented for the hard core square well fluid and for the restricted primitive model electrolyte including an estimate of the correlation exponent ensuremath nu that confirms ising type character the treatment is extended to the canonical representation where further complications appear

exact results for the asymmetric simple exclusion process with a blockage we present new results for the current as a function of transmission rate in the one dimensional totally asymmetric simple exclusion process tasep with a blockage that lowers the jump rate at one site from one tor 1 exact finitevolume results serve to bound the allowed values for the current in the infinite system this proves the existence of a nonequilibrium phase transition corresponding to an immiscibility gap in the allowed values of the asymptotic densities which the infinite system can have in a stationary state a series expansion inr derived from the finite systems is proven to be asymptotic for all sufficiently large systems pade approximants based on this series which make specific assumptions about the nature of the singularity atr 1 match numerical data for the infinite system to 1 part in 104

generalized structured component analysis with latent interactions generalized structured component analysis gsca is a component based approach to structural equation modeling in practice researchers may often be interested in examining the interaction effects of latent variables however gsca has been geared only for the specification and testing of the main effects of variables thus an extension of gsca is proposed to effectively deal with various types of interactions among latent variables in the proposed method a latent interaction is defined as a product of interacting latent variables as a result this method does not require the construction of additional indicators for latent interactions moreover it can easily accommodate both exogenous and endogenous latent interactions an alternating least squares algorithm is developed to minimize a single optimization criterion for parameter estimation a monte carlo simulation study is conducted to investigate the parameter recovery capability of the proposed method an application is also presented to demonstrate the empirical usefulness of the proposed method

multicanonical monte carlo simulations canonical monte carlo simulations of disordered systems like spin glasses and systems undergoing first order phase transitions are severely hampered by rare event states which lead to exponentially diverging autocorrelation times with increasing system size and hence to exponentially large statistical errors one possibility to overcome this problem is the multicanonical reweighting method using standard local update algorithms it could be demonstrated that the dependence of autocorrelation times on the system size v is well described by a less divergent power law v with 1 3 depending on the system after a brief review of the basic ideas combinations of multicanonical reweighting with non local update algorithms will be discussed with the multibondic algorithm which combines multicanonical reweighting with cluster updates the dynamical exponent can be reduced to unity the optimal value one would expect from a random walk argument asymptotically for large system sizes the multibondic algorithm therefore always performs better than the standard multicanonical method finally it is shown that a combination with multigrid update techniques improves the performance of multicanonical simulations by roughly one order of magnitude uniformly for all system sizes

critical behavior in colloid polymer mixtures theory and simulation we extensively investigated the critical behavior of mixtures of colloids and polymers via the two component asakura oosawa model and its reduction to a one component colloidal fluid using accurate theoretical and simulation techniques in particular the theoretical approach hierarchical reference theory a parola and l reatto adv phys 44 211 1995 incorporates realistically the effects of long range fluctuations on phase separation giving exponents which differ strongly from their mean field values and are in good agreement with those of the three dimensional ising model computer simulations combined with finite size scaling analysis confirm the ising universality and the accuracy of the theory although some discrepancy in the location of the critical point between one component and full mixture description remains to assess the limit of the pair interaction description we compare one component and two component results

monte carlo study of the random field ising model using a cluster flipping monte carlo algorithm combined with a generalization of the histogram reweighting scheme of ferrenberg and swendsen we have studied the equilibrium properties of the thermal random field ising model on a cubic lattice in three dimensions we have equilibrated systems of l x l x l spins with values of l up to 32 and for these systems the cluster flipping method appears to a large extent to overcome the slow equilibration seen in single spin flip methods from the results of our simulations we have extracted values for the critical exponents and the critical temperature and randomness of the model by finite size scaling for the exponents we find v 1 02 0 06 b 0 06 0 07 y 1 9 0 2 and mean y 2 9 0 2

determining the density of states for classical statistical models a random walk algorithm to produce a flat histogram we describe an efficient monte carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models the density of states is modified at each step when the energy level is visited to produce a flat histogram by carefully controlling the modification factor we allow the density of states to converge to the true value very quickly even for large systems from the density of states at the end of the random walk we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature using this method we not only can avoid repeating simulations at multiple temperatures but we can also estimate the free energy and entropy quantities that are not directly accessible by conventional monte carlo simulations this algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability as with the multicanonical monte carlo technique our method overcomes the tunneling barrier between coexisting phases at first order phase transitions in this paper we apply our algorithm to both first and second order phase transitions to demonstrate its efficiency and accuracy we obtained direct simulational estimates for the density of states for two dimensional ten state potts models on lattices up to 200 x 200 and ising models on lattices up to 256 x 256 our simulational results are compared to both exact solutions and existing numerical data obtained using other methods applying this approach to a three dimensional j spin glass model we estimate the internal energy and entropy at zero temperature and using a two dimensional random walk in energy and order parameter space we obtain the rough canonical distribution and energy landscape in order parameter space preliminary data suggest that the glass transition temperature is about 1 2 and that better estimates can be obtained with more extensive application of the method this simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space

understanding and improving the wang landau algorithm we present a mathematical analysis of the wang landau algorithm prove its convergence and identify sources of errors and strategies for optimization in particular we found the histogram increases uniformly with small fluctuations after a stage of initial accumulation and the statistical error is found to scale as sqrt mathrm ln phantom rule 0 2em 0ex f with the modification factor f this has implications for strategies for obtaining fast convergence

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

first order transition in the one dimensional three state potts model with long range interactions the first order phase transition in the three state potts model with long range interactions decaying as 1 r 1 ensuremath sigma has been examined by numerical simulations using the recently proposed luijten bl ote algorithm by applying scaling arguments to the interface free energy the binder s fourth order cumulant and the specific heat maximum the change in the character of the transition through variation of parameter ensuremath sigma was studied

the critical behaviour of the long range potts chain from the largest cluster probability distribution abstract we present the numerical study of the one dimensional potts model with power law decaying ferromagnetic interactions the largest cluster probability distribution is obtained by monte carlo simulations using the swendsen wang cluster algorithm with cumulative probabilities the finite size scaling analysis of the largest cluster is used to derive the critical behaviour in the non classical regime of this model for various values of q

one dimensional ising models with long range interactions we consider ising models with long range ferromagnetic pair interactions decaying as for we first find approximate values for the critical temperature we use a cluster mean field approach combined with finite size scaling and vanden broeck and schwartz transformations for we find which can be compared with recent results of luijten and blote who found and which is two orders of magnitude more accurate than any previous results since we use a mean field cluster approximation as part of our approach the accuracy for larger values of decreases significantly in addition to we obtain approximate values for the critical exponents and using the coherent anomaly method for we obtain and all extremely close to the predictions of renormalization group calculations which say that these exponents should take on their classical values for this value of

critical behavior of a colloid polymer mixture confined between walls we investigate the influence of confinement on phase separation in colloid polymer mixtures to describe the particle interactions the colloid polymer model of asakura and oosawa j chem phys 22 1255 1954 is used grand canonical monte carlo simulations are then applied to this model confined between two parallel hard walls separated by a distance d 5 colloid diameters we focus on the critical regime of the phase separation and look for signs of crossover from three dimensional 3d ising to two dimensional 2d ising universality to extract the critical behavior finite size scaling techniques are used including the recently proposed algorithm of kim et al phys rev lett 91 065701 2003 our results point to effective critical exponents that differ profoundly from 3d ising values and that are already very close to 2d ising values in particular we observe that the critical exponent of the order parameter in the confined system is smaller than in 3d bulk yielding a flatter binodal our results also show an increase in the critical colloid packing fraction in the confined system with respect to the bulk the latter seems consistent with theoretical expectations although subtleties due to singularities in the critical behavior of the coexistence diameter cannot be ruled out

t 0 finite size scaling for a quantum system with long range interaction abstract the general idea of finite size scaling are tested by the example of the pure quantum version of an exactly solvable model of structural phase transition with long range interaction decaying at large distances r as r d where d is the space dimensionality and 0 the finite size shift of the quantum parameter playing the same role as that of the temperature for classical systems is calculated for the general geometry ld d d with 0 0 2

monte carlo investigations of phase transitions status and perspectives abstract using the concept of finite size scaling monte carlo calculations of various models have become a very useful tool for the study of critical phenomena with the system linear dimension as a variable as an example several recent studies of ising models are discussed as well as the extension to models of polymer mixtures and solutions it is shown that using appropriate cluster algorithms even the scaling functions describing the crossover from the ising universality class to the mean field behavior with increasing interaction range can be described additionally the issue of finite size scaling in ising models above the marginal dimension d 4 is discussed

generalized mittag leffler functions in the theory of finite size scaling for systems with strong anisotropy and or long range interaction the difficulties arising in the investigation of finite size scaling in d dimensional o n systems with strong anisotropy and or long range interaction decaying with the interparticle distance r as r d 0 2 are discussed some integral representations aiming at the simplification of the investigations are presented for the classical and quantum lattice sums that take place in the theory special attention is paid to a more general form allowing to treat both cases on an equal footing and in addition cases with strong anisotropic interactions and different geometries the analysis is simplified further by expressing this general form in terms of a generalization of the mittag leffler special functions this turned out to be very useful for the extraction of asymptotic finite size behaviours of the thermodynamic functions

differentiation to fractional orders and the fractional telegraph equation using methods of differential and integral calculus we present and discuss the calculation of a fractional green function associated with the one dimensional case of the so called general fractional telegraph equation with one space variable this is a fractional partial differential equation with constant coefficients the equation is solved by means of juxtaposition of transforms i e we introduce the laplace transform in the time variable and the fourier transform in the space variable several particular cases are discussed in terms of the parameters some known results are recovered as a by product of our main result we obtain two new relations involving the two parameter mittag leffler function

long range one dimensional potts models a cluster mean field and extrapolation approach we obtain approximations for the critical temperature tc of q state ferromagnetic potts models on one dimensional lattices with algebraically decaying ferromagnetic pair interactions i e decaying as 1 r with 1 2 initially we use a cluster mean field method to get approximations to the critical temperature and we look at increasingly large clusters this gives us a sequence of ever more accurate approximate values which can be used as input to various extrapolation algorithms we see that as the interaction decreases more slowly and the value of q increases we obtain more and more accurate tc estimates our best estimates we believe to be correct to four figure accuracy

finite size scaling for the mean spherical model with inverse power law interaction a new analytical technique based on integral transformations with mittag leffler type kernels is used to derive the finite size scaling function for the free energy per particle of the mean spherical model with inverse power law asymptotics of the interaction potential the asymptotic formation of the singularities in the specific heat and magnetic susceptibility at the bulk critical point is studied

test of renormalization predictions for universal finite size scaling functions we calculate universal finite size scaling functions for systems with an n component order parameter and algebraically decaying interactions just as previously found for short range interactions this leads to a singular ensuremath varepsilon expansion where ensuremath varepsilon is the distance to the upper critical dimension subsequently we check the results by numerical simulations of spin models in the same universality class our systems offer the essential advantage that ensuremath varepsilon can be varied continuously allowing an accurate examination of the region where ensuremath varepsilon is small the numerical calculations turn out to be in striking disagreement with the predicted singularity

the one dimensional potts model with long range interactions a renormalization group approach the one dimensional q state potts model with ferromagnetic pair interactions which decay with the distance r as is considered we calculate through a real space renormalization group technique using kadanoff blocks of length b the critical temperature and the correlation length critical exponent as a function of for different values of q some of the very few known rigorous results for general q are reproduced by our approach several asymptotic behaviours are derived analytically for q 2 3 in the limit we also obtain extrapolated critical temperatures for arbitrary values of and for q 2 3 4 which we believe approximate the exact ones well except in the region near furthermore the use of another extrapolation procedure suitable only in the vicinity of led us to conjecture that the exact critical temperature is the same for any value of q we also verify that which is consistent with a recent conjecture of tsallis

fast flat histogram method for generalized spin models we present a monte carlo method that efficiently computes the density of states for spin models having any number of interaction per spin by combining a random walk in the energy space with collective updates controlled by the microcanonical temperature our method yields dynamic exponents close to their ideal random walk values reduced equilibrium times and very low statistical error in the density of states the method can host any density of states estimation scheme including the wang landau algorithm and the transition matrix method our approach proves remarkably powerful in the numerical study of models governed by long range interactions where it is shown to reduce the algorithm complexity to that of a short range model with the same number of spins we apply the method to the q state potts chains 3 ensuremath leqslant q ensuremath leqslant 12 with power law decaying interactions in their first order regime we find that conventional local update algorithms are outperformed already for sizes above a few hundred spins by considering chains containing up to 2 16 spins which we simulated in fairly reasonable time we obtain estimates of transition temperatures correct to five figure accuracy finally we propose several efficient schemes aimed at estimating the microcanonical temperature

critical behaviour of the 1d q state potts model with long range interactions the critical behaviour of the one dimensional q state potts model with long range interactions decaying with distance r as r 1 sigma has been studied in the wide range of parameters 0 sigma or 1 and 1 16 or q or 64 a transfer matrix has been constructed for a truncated range of interactions for integer and continuous q and finite range scaling has been applied results for the phase diagram and the correlation length critical exponent are presented

on the symmetry of universal finite size scaling functions in anisotropic systems we postulate a symmetry of universal finite size scaling functions under a certain anisotropic scale transformation which connects the properties of a finite two dimensional 2d system at criticality with generalized aspect ratio 1 to a system with 1 the symmetry is formulated within a finite size scaling theory and expressions for several universal amplitude ratios are derived the predictions are confirmed within the exactly solvable weakly anisotropic 2d ising model and are checked within the strongly anisotropic 2d dipolar in plane ising model using monte carlo simulations

three mode factor analysis by means of candecomp parafac a three mode covariance matrix contains covariances of n observations e g subject scores on j variables for k different occasions or conditions we model such an jk jk covariance matrix as the sum of a common covariance matrix having candecomp parafac form and a diagonal matrix of unique variances the candecomp parafac form is a generalization of the two mode case under the assumption of parallel factors we estimate the unique variances by minimum rank factor analysis the factors can be chosen oblique or orthogonal our approach yields a model that is easy to estimate and easy to interpret moreover the unique variances the factor covariance matrix and the communalities are guaranteed to be proper a percentage of explained common variance can be obtained for each variable condition combination and the estimated model is rotationally unique under mild conditions we apply our model to several datasets in the literature and demonstrate our estimation procedure in a simulation study

a statistical theory to aggregation in one dimensional freeway traffic the master equation of the car cluster in freeway traffic is reinvestigated on the basis of the linear assumption of the transition in which the dynamic behavior of the cluster in a one lane freeway traffic flow is studied the expression of the mean size of the cluster versus t is derived in term of the solution of the birth death equation we also obtain the analytical expression of the probability distribution p n t numerical simulations testify the results derived as well

pseudo maximum likelihood estimation of mean and covariance structures with missing data abstract a nonlinear mean and covariance structure model for one or more groups is constructed the model subsumes the usual linear model considered in the literature it is then shown how to estimate the parameters of the model and the asymptotic covariance matrix of the parameter estimates using pseudo maximum likelihood pml estimation the resulting estimates are strongly consistent under general regularity conditions provided only that the model for the first two moments is correctly specified nevertheless because the data are not necessarily drawn from a multivariate normal distribution the usual likelihood ratio tests for model comparisons in mean and covariance structure models do not apply wald tests and lagrange multiplier tests may be used to implement such comparisons next the standard results on ml estimation with missing data are extended to the case of pml estimation with missing data and the results are applied to the model the approach to the missing data problem adopted whic

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

reexamination of the long range potts model a multicanonical approach we investigate the critical behavior of the one dimensional q state potts model with long range lr interaction 1 r d sigma using a multicanonical algorithm the recursion scheme initially proposed by berg is improved so as to make it suitable for a large class of lr models with unequally spaced energy levels the choice of an efficient predictor and a reliable convergence criterion is discussed we obtain transition temperatures in the first order regime which are in far better agreement with mean field predictions than in previous monte carlo studies by relying on the location of spinodal points and resorting to scaling arguments we determine the threshold value sigma c q separating the first and second order regimes to two digit precision within the range 3 leq q leq 9 we offer convincing numerical evidence supporting sigma c q 1 0 for all q by virtue of an unusual finite size effect namely finite size scaling predicts a continuous transition in the thermodynamic limit despite the first order nature of the transition at finite size a qualitative account in terms of correlation lengths is provided finally we find the crossover between the lr and short range regimes to occur inside a narrow window 1 0 sigma 1 2 thus lending strong support to sak s scenario

methods for mediation analysis with missing data despite wide applications of both mediation models and missing data techniques formal discussion of mediation analysis with missing data is still rare we introduce and compare four approaches to dealing with missing data in mediation analysis including listwise deletion pairwise deletion multiple imputation mi and a two stage maximum likelihood ts ml method an r package bmem is developed to implement the four methods for mediation analysis with missing data in the structural equation modeling framework and two real examples are used to illustrate the application of the four methods the four methods are evaluated and compared under mcar mar and mnar missing data mechanisms through simulation studies both mi and ts ml perform well for mcar and mar data regardless of the inclusion of auxiliary variables and for av mnar data with auxiliary variables although listwise deletion and pairwise deletion have low power and large parameter estimation bias in many studied conditions they may provide useful information for exploring missing mechanisms

advanced structural equation modeling issues and techniques contents g a marcoulides r e schumacker introduction w wothke models for multitrait multimethod matrix analysis k g joreskog f yang nonlinear structural equation models the kenny judd model with interaction effects j j mcardle f hamagami multilevel models from a multiple group structural equation perspective j b willett a g sayer cross domain analyses of change over time combining growth modeling and covariance structure analysis s l hershberger p c m molenaar s e corneal a hierarchy of univariate and multivariate structural times series models y f yung p m bentler bootstrapping techniques in analysis of mean and covariance structures k a bollen a limited information estimator for lisrel models with or without heteroscedastic errors j l arbuckle full information estimation in the presence of incomplete data l j williams h bozdogan l aiman smith inference problems with equivalent models h w marsh j r balla k t hau an evaluation of incremental fit indices a clarification of mathematical and empirical properties

dynamical behavior of the multibondic and multicanonic algorithm in the 3d q state potts model we investigate the dynamical behavior of the recently proposed multibondic cluster monte carlo algorithm in applications to the three dimensional q state potts models with q 3 4 and 5 in the vicinity of their first order phase transition points for comparison we also report simulations with the standard multicanonical algorithm similar to the findings in two dimensions we show that for the multibondic cluster algorithm the dependence of the autocorrelation time on the system size vis well described by the power law v and that the dynamical exponent is consistent with the optimal random walk estimate 1 for the multicanonical simulations we obtain as expected a larger value of 1 2

revisiting universality of the liquid gas critical point in two dimensions critical point of liquid gas lg transition does not conform with the paradigm of spontaneous symmetry breaking because there is no broken symmetry in both phases we revisit the conjecture that this critical point belongs to the ising class by performing large scale monte carlo simulations in two dimensional free space in combination with the numerical flowgram method our main result is that the critical indices do agree with the onsager values within the error of 1 2 this significantly improves the accuracy reported in the literature the related problem about the role of higher order odd terms in the real ensuremath varphi 4 field model as a mapping of the lg transition is addressed too the scaling dimension of the ensuremath varphi 5 term at criticality is shown to be the same as that of the linear one ensuremath varphi we suggest that the role of all higher order odd terms at criticality is simply in generating the linear field operator with the critical dimension consistent with the ising universality class

overcoming the slowing down of flat histogram monte carlo simulations cluster updates and optimized broad histogram ensembles we study the performance of monte carlo simulations that sample a broad histogram in energy by determining the mean first passage time to span the entire energy space of d dimensional ferromagnetic ising potts models we first show that flat histogram monte carlo methods with single spin flip updates such as the wang landau algorithm or the multicanonical method perform suboptimally in comparison to an unbiased markovian random walk in energy space for the d 1 2 3 ising model the mean first passage time ensuremath tau scales with the number of spins n l d as ensuremath tau ensuremath propto n 2 l z the exponent z is found to decrease as the dimensionality d is increased in the mean field limit of infinite dimensions we find that z vanishes up to logarithmic corrections we then demonstrate how the slowdown characterized by zg0 for finite d can be overcome by two complementary approaches char22 cluster dynamics in connection with wang landau sampling and the recently developed ensemble optimization technique both approaches are found to improve the random walk in energy space so that ensuremath tau ensuremath propto n 2 up to logarithmic corrections for the d 1 2 ising model

critical finite size scaling of the free energy the privman fisher universal amplitude characterizing the free energy of a finite sized system at its critical point is identified as the critical counterpart of the number of stable phases on the coexistence curve its value is shown to be determined by the critical point form of the order parameter distribution directly accessible to monte carlo studies

moment testing for interaction terms in structural equation modeling starting with kenny and judd psychol bull 96 201 210 1984 several methods have been introduced for analyzing models with interaction terms in all these methods more information from the data than just means and covariances is required in this paper we also use more than just first and second order moments however we are aiming to adding just a selection of the third order moments the key issue in this paper is to develop theoretical results that will allow practitioners to evaluate the strength of different third order moments in assessing interaction terms of the model to select the third order moments we propose to be guided by the power of the goodness of fit test of a model with no interactions which varies with each selection of third order moments a theorem is presented that relates the power of the usual goodness of fit test of the model with the power of a moment test for the significance of third order moments the latter has the advantage that it can be computed without fitting a model the main conclusion is that the selection of third order moments can be based on the power of a moment test thus assessing the relevance in the analysis of different sets of third order moments can be computationally simple the paper gives an illustration of the method and argues for the need of refraining from adding into the analysis an excess of higher order moments

on the asymptotic relative efficiency of planned missingness designs in planned missingness pm designs certain data are set a priori to be missing pm designs can increase validity and reduce cost however little is known about the loss of efficiency that accompanies these designs the present paper compares pm designs to reduced sample rn designs that have the same total number of data points concentrated in fewer participants in 4 studies we consider models for both observed and latent variables designs that do or do not include an x set of variables with complete data and a full range of between and within set correlation values all results are obtained using asymptotic relative efficiency formulas and thus no data are generated this novel approach allows us to examine whether pm designs have theoretical advantages over rn designs removing the impact of sampling error our primary findings are that a in manifest variable regression models estimates of regression coefficients have much lower relative efficiency in pm designs as compared to rn designs b relative efficiency of factor correlation or latent regression coefficient estimates is maximized when the indicators of each latent variable come from different sets and c the addition of an x set improves efficiency in manifest variable regression models only for the parameters that directly involve the x set variables but it substantially improves efficiency of most parameters in latent variable models we conclude that pm designs can be beneficial when the model of interest is a latent variable model recommendations are made for how to optimize such a design

fractal structure of spin clusters and domain walls in the two dimensional ising model the fractal structure of spin clusters and their boundaries in the critical two dimensional ising model is investigated numerically the fractal dimensions of these geometrical objects are estimated by means of monte carlo simulations on relatively small lattices through standard finite size scaling the obtained results are in excellent agreement with theoretical predictions and partly provide significant improvements in precision over existing numerical estimates

stochastic master equation approach to aggregation in freeway traffic in analogy to the usual aggregation phenomena such as the formation of liquid droplets in a supersaturated vapor the nucleation growth and condensation of car clusters are considered in a one lane freeway traffic flow model the clustering behavior known as congestion in an initially homogeneous traffic stream is described by a master equation the construction of the stochastic equation is given as well as its relationship to other dynamical models numerical experiments in heavy traffic with well explained transition probabilities show the transition from the initial free particle situation free jet of vehicles to the final congested cluster state where one big aggregate of cars is formed the results are presented analytically in dependence of the stable cluster size from car concentration and numerically as stochastic trajectories

design and analysis of incomplete multitrait multimethod studies from a multiplicative perspective the composite direct product cdp model is a multiplicative model for multitrait multimethod mtmm designs it is extended to incomplete mtmm correlation matrices where some trait method combinations are not available rules for omitting trait method combinations without resulting in an indeterminate model are also suggested maximum likelihood estimation and the log absolute correlation procedure are used to fit the model and are found to yield similar results the balanced incomplete mtmm design tends to yield more accurate estimates than the randomly missing design

localized defects in a cellular automaton model for traffic flow with phase separation the impact of a localized defect in a cellular automaton model for traffic flow which exhibits metastable states and phase separation is studied the defect is implemented by locally increasing the deceleration probability depending on the magnitude three phases can be identified in the system one of them shows the characteristics of stop and go traffic which can not be found in the model without lattice defect from a physical point of view the model describes the competition between two mechanisms of phase separation

the investigation of the reentrance phenomenon in cellular automaton traffic flow model abstract we investigate analytically and by numerical simulations the reentrant low density phase for high injection rate in the nagel schreckenberg model it is found that the reentrance phenomenon is a direct consequence of our injection strategy indeed by adopting our injection rule an injection rate exists above which the in flow begins to decrease by increasing the injection rate in addition we have studied the extraction rate interval at which the reentrance of the low density phase appears it is found that this interval increases with increasing the maximal velocity for the non deterministic case the reentrance interval shifts to higher values of extraction rate

the correlation length of the potts model at the first order transition point the authors consider the q state two dimensional potts model for q g i e in the first order phase transition regime following a scheme given by p martin 1991 the authors prove an identity between the spectra of the transfer matrices of the potts model and the transfer matrices connecting the diagonals of a 6 vertex model by using a bethe ansatz for the latter they obtain an exact expression for the correlation length of the potts model at the transition point

an improved cellular automaton traffic model considering gap dependent delay probability abstract in this paper the delay probability of the original nagel and schreckenberg model is modified to simulate one lane traffic flow the delay probability of a vehicle depends on its corresponding gap according to simulation results it has been found that the structure of the fundamental diagram of the new model is sensitively dependent on the values of the delay probability in comparison with the ns model one notes that the fundamental diagram of the new model is more consistent with the results measured in the real traffic and the velocity distributions of the new model are relatively reasonable

convergence of finite size scaling renormalisation techniques abstract the rate of convergence of the transfer matrix finite size scaling or phenomenological renormalisation method is studied it is shown both heuristically and numerically that the convergence of estimates for exponents etc is governed asymptotically by the leading irrelevant variable scaling exponent the more rapid apparent convergence rates observed in many practical calculations for two dimensional lattices of widths up to ten lattice spacings are attributed to cancellation between various correction terms

ising universality in three dimensions a monte carlo study we investigate three ising models on the simple cubic lattice by means of monte carlo methods and finite size scaling these models are the spin 1 2 ising model with nearest neighbour interactions a spin 1 2 model with nearest neighbour and third neighbour interactions and a spin 1 model with nearest neighbour interactions the results are in accurate agreement with the hypothesis of universality analysis of the finite size scaling behaviour reveals corrections beyond those caused by the leading irrelevant scaling field we find that the correction to scaling amplitudes are strongly dependent on the introduction of further neighbour interactions or a third spin state in a spin 1 ising model these corrections appear to be very small this is very helpful for the determination of the universal constants of the ising model the renormalization exponents of the ising model are determined as yt 1 587 2 yh 2 4815 15 and yi 0 82 6 the universal ratio q m2 2 m4 is equal to 0 6233 4 for periodic systems with cubic symmetry the critical point of the nearest neighbour spin 1 2 model is kc 0 2216546 10

optimized energy calculation in lattice systems with long range interactions we discuss an efficient approach to the calculation of the internal energy in numerical simulations of spin systems with long range interactions although since the introduction of the luijten blote algorithm monte carlo simulations of these systems no longer pose a fundamental problem the energy calculation is still an o n 2 problem for systems of size n we show how this can be reduced to an o n log n problem with a break even point that is already reached for very small systems this allows the study of a variety of until now hardly accessible physical aspects of these systems in particular we combine the optimized energy calcula tion with histogram interpolation methods to investigate the specific heat of the ising model and the first order regime of the three state potts model with long range interactions

the comparative efficacy of imputation methods for missing data in structural equation modeling abstract missing data is a problem that permeates much of the research being done today traditional techniques for replacing missing values may have serious limitations recent developments in computing allow more sophisticated techniques to be used this paper compares the efficacy of five current and promising methods that can be used to deal with missing data this efficacy will be judged by examining the percent of bias in estimating parameters the focus of this paper is on structural equation modeling sem a popular statistical technique which subsumes many of the traditional statistical procedures to make the comparison this paper examines a full structural equation model that is generated by simulation in accord with previous research the five techniques used for comparison are expectation maximization em full information maximum likelihood fiml mean substitution mean multiple imputation mi and regression imputation regression all of these techniques other than fiml impute missing data and result in a complete dataset that can be used by researchers for other research fiml on the other hand can still estimate the parameters of the model the study involves two levels of sample size 100 and 500 and seven levels of incomplete data 2 4 8 12 16 24 and 32 missing completely at random after extensive bootstrapping and simulation the results indicate that fiml is a superior method in the estimation of most different types of parameters in a sem format furthermore mi is found to be superior in the estimation of standard errors multiple imputation mi also is an excellent estimator with the exception of datasets with over 24 missing information considering the fact that fiml is a direct method and does not actually impute the missing data whereas mi does and can yield a complete set of data for the researcher to analyze we conclude that mi because of its theoretical and distributional underpinnings is probably most promising for future applications in this field