PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

A review of regression analysis methods: Establishing thequantitative relationships between subjective soundscapeassessment and multiple factors
Ming YANG1
1

HEAD Genuit Foundation, Germany

ABSTRACTSoundscape research has long been exploring factors/indicators that would impact human perception,
emotional assessment, behaviour, etc. Since soundscape is intrinsically a complex system, a wide variety offactors have been suggested by intensive studies and also ISO/TS 12913-2 standard, ranging from acoustics,
psychoacoustics, sound source composition, to demographics, and other personal/social/cultural factors. To
examine subsequently the quantitative relationships between such factors and impacts/effects of soundscape,data statistical methods are essential. A wide range of statistical methods have been commonly used insoundscape studies corresponding to different specific research tasks, e.g. correlation analysis, analysis ofvariance, factor analysis and cluster analysis. While soundscape is affected by not only any single factor but
multiple factors simultaneously and interactively, this paper focuses on a statistical method, regression
analysis, that can investigate multiple variables to study the relationships and predict soundscape effects frommultiple possible factors. This paper provides a brief review of a set of regression analysis methods, which
are used for analysing different types of variables, e.g. continuous, ordinal and nominal. It then exemplifies
the methods with a number of regression models from previous soundscape studies, particularly on
subjective soundscape assessments (namely soundscape descriptors, e.g. pleasantness, satisfaction, andcomfort), which is a crucial part in soundscape research.
Keywords: Soundscape, Regression analysis, Multiple variables

1. INTRODUCTION
Soundscape research has suggested that sound environments have impacts on human perception,
cognition, emotion, behaviour, health and well-being, etc. (1). Soundscape studies investigated suchimpacts/effects due to different sound environments (2). For example, a large number of soundscapestudies focused on people’s subjective perceptual and emotional responses/assessments of soundenvironments, such as pleasantness, satisfaction, and comfort, which were defined as soundscapedescriptors in ISO/TS 12913-2 standard (3), and formed a substantial part of soundscape research.
The effects of sound environments would be caused by a wide variety of environmental factors, aswell as human factors that might explain the individual differences in responses. The factors, exploredby previous soundscape studies and suggested by ISO/TS 12913-2 standard (3), include acoustic andpsychoacoustic indicators (e.g. equivalent sound pressure level LAeq and LCeq, percentage
exceedance levels LA5 and LA95, psychoacoustic loudness, sharpness, tonality, roughness, andfluctuation strength) (4), sound source compositions, visual factors of environment, demographic
factors (e.g. age and gender) and other personal/social/cultural factors.
Soundscape research attempts to establish the relationships between the soundscape effects andfactors, to study the influences of the factors on various soundscape effects, or to predict soundscapeeffects/responses from the factors (e.g. use indicators to predict soundscape descriptors). To achievethese in a quantitative way, data statistical methods are essential. A wide range of statistical methods
have been used in soundscape studies according to different specific research tasks, e.g. correlation
analysis, analysis of variance, factor analysis and cluster analysis. Since soundscape is intrinsically acomplex system, effects of sound environments are caused by not only any single factor but multiple
factors simultaneously and interactively. To study such relationships, statistical methods that can deal
1

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mingkateyang@163.com

with multiple variables need to be used.
Among the statistical methods or machine learning methods that can investigate multiple variables,e.g. regression analysis, fuzzy logic model and artificial neural network, this paper focuses onregression analysis which have been commonly used in soundscape studies. The following of thispaper firstly discusses the types of variables (for both impacts and factors), and then provides a brief
review of the regression methods for analysing the different types of variables. Finally, it exemplifies
the methods with a number of regression models of subjective soundscape assessments, namely
soundscape descriptors, from previous soundscape studies.

2. SOUNDSCAPE VARIABLES (E.G. DESCRIPTORS AND INDICATORS)
In statistics, a variable is something that varies between individuals or items. All the soundscape
impacts and factors can be variables. The variables to be studied or predicted by other variables arecalled dependent variables, frequently the soundscape impacts or soundscape descriptors. The
variables used as factors to predict the dependent variables are called independent variables,
frequently the acoustic and psychoacoustic indicators or other soundscape descriptors. Statisticalmethods attempt to analyse the relationships between variables or the effects of independent variables
on dependent variables.
There are several types of variables, in general categorical and numeric. Categorical variables arealso known as discrete or qualitative variables. Categorical variables can be further categorised aseither binary, nominal, or ordinal. Binary or dichotomous variables are variables which have only two
categories or levels, such as true/false, yes/no (coded by an indicator variable 1/0). Nominal variables
are variables that have two or more categories, but which do not have an intrinsic order.
Ordinal variables are variables that have two or more categories just like nominal variables only thecategories can also be ordered or ranked. Numeric variables are also known as quantitative variables,
and are either discrete or continuous. Discrete variables can take only a distinct number of values,
often integers for such as count. Continuous variables can take any real value number within a certain
range, either interval or ratio. There are overlaps between the different types of variable, e.g. there
may be dispute about whether an integer variable is discrete numeric or ordinal. In addition, variables
can sometimes be deliberately rearranged from one type to another, e.g. age (continuous variable) can
be changed to age group (ordinal variable) (5).
Table 1 gives some examples of the types of variables used in soundscape research. It is worth
noting that in some cases, variables can be treated as different types. The choice of the type of avariable somehow depends on the case.
Table 1 – Examples of variable types in soundscape researchContinuousInterval/ratio
Soundscape

11-point / 7- point

Categorical
BinaryNominalOrdinal•descriptors (e.g.
by semantic•

5-point

differential)
Acoustic andLAeq / LCeq / LA5 / LA95 /psychoacoustic

loudness/ sharpness / tonality /indicatorsroughness / fluctuation strength

Sound source

Whether a source present or notcompositions

Perceived loudness of a source•

Age group•

Demographic
factors

GenderProfession

•
•

•
•

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3. STATISTICAL METHODS: REGRESSION ANALYSIS
Regression analysis is a set of statistical methods that estimate the relationship between dependent
variables (Y) and independent variables (X). It produces a function of one or more independent
variables (with the parameters) called the regression function or regression model, to estimate thedependent variable(s). Regression analysis can be used for indicating the effects of independent
variables on dependent variables, finding the causal relationship between the variables, and predicting
the dependent variables given the independent variables. Regression analysis is one of thefundamental algorithms in the field of machine learning (6).
The following describes a number of regression methods that have been or would be used insoundscape research, according to the number and type of variables.
3.1 Linear Regression
Linear regression is one of the most widely used regression analysis in practical applications.
Linear regression specifies that the dependent variable is a linear combination of the parameters (butneed not be linear in the independent variables). The case of one independent variable is called simple
linear regression. When there are more than one independent variable or function of independent
variable(s), it is called multiple linear regression.
Linear regression attempts to establish a relationship between a dependent variable and one or more
independent variables by fitting a linear equation (e.g. a straight line) to observed data. The equation
is in the form Y=a+b*X, where a is the intercept (a constant term) and b is the slope of the line.
The regression can be understood simply as finding the parameters of the equation that best fit theobserved data. The most common method for calculating the best-fitting line for linear regression is
the method of least squares. This method obtains parameter estimates by minimizing the sum ofsquared residuals of all data, where the residual is the difference between the predicted value of thedependent variable by the model and the true value of the dependent variable (6).
In linear regression, the dependent variable is continuous, whereas independent variable(s) can
be continuous or discrete, such as binary, nominal or ordinal.
3.2 Logistic Regression
Logistic regression (also called logit regression) is a regression analysis in its basic form used forpredicting a binary dependent variable rather than a continuous dependent variable in linear regression.
Logistic regression calculates the probability of dependent variable being a case or being a non-case(7).
As a generalized linear regression, what logistic regression does is to convert a binary dependent
variable into a continuous one, and simulate the continuous one through a linear regression. To do this,logistic regression takes the logit function log[p/(1−p)], where p is the probability, (i.e. the logarithmof the odds (log-odds) where the odds are defined as the probability of being a case divided by theprobability of being a non-case), to create a continuous criterion as a transformed version of thedependent variable, and then calculates the log-odds through a linear combination of one or more
independent variables. After that, it converts the predicted value of the log-odds back into predictedprobability via the inverse of the logit function, namely a logistic function (a sigmoid function), andoutputs a value between zero and one. The regression parameters are usually estimated using
maximum likelihood estimation.
The logistic regression model itself simply calculates probability of output, and does not performstatistical classification, though by choosing a cut-off value of probability it can be used to make aclassification.
The binomial or binary logistic regression has extensions to more than two levels of the dependent
variable: categorical outputs with more than two values are modelled by multinomial logistic
regression, and if the multiple categories are ordered, by ordinal logistic regression.
Like other forms of regression analysis, the independent variables of logistic regression can each beeither continuous or categorical.
3.3 Probit Regression
Analogous to logistic regression, probit regression is also used to predict a binary dependent
variable. However, probit regression and logistic regression use different link functions (sigmoid
functions) to transform the binary dependent variable into a continuous latent variable. Instead of thelogit function in logistic regression, probit regression uses an inverse standard normal distribution of6124

probability and models the latent variable as a linear combination of independent variables.
3.4 Multivariate Regression
Unlike the regression methods above which predict one dependent variable, multivariate regression
is a regression method of modelling multiple dependent variables. It estimates the relationship of the
independent variables with each dependent variable, in a similar way to regressing each dependent
variable separately.

4. PREDICTION MODELS OF SUBJECTIVE SOUNDSCAPE ASSESSMENTS
Among various soundscape effects, such as perception, emotion, behaviour, health and well-being,
a number of regression models of subjective perceptual/emotional assessments (as a substantial part insoundscape research) from previous soundscape studies are presented in this section, as application
examples of the above regression analysis methods.
4.1

Multiple Linear Regression Model

4.1.1 Sound Quality in Terms of Pleasantness
Ricciardi et al (8) used multiple linear regression to model the perceived sound quality(pleasantness) of soundscape from other perceptual variables. They collected perceptual data from alarge number (3409) of participants in Paris via smartphone applications. When a participant visited adefined location at a defined time (with the GPS and time information recorded on the mobiles), thesound pressure levels were recorded and the participant answered a questionnaire covered question
items in three categories based on 11-point bipolar semantic scales. The first category was related tothe overall sound environment: Overall loudness (OL), which described the perceived sound level ofthe sound environment at the location, from “quiet” to “loud”; Liveliness (L), from “lifeless” to“lively”; Not enveloping (NE), from “enveloping” to “not enveloping”, Sound quality (SQ), from
“unpleasant” to “pleasant”; Visual amenity (VA), from “unpleasant” to “pleasant”, and Familiarity (F),from “unfamiliar” to “familiar”. The second category described the emergent sound sources: perceived
loudness of such as mopeds (PLM), cars (PLC), horns and sirens (PLH), trucks (PLT) and buses (PLB),
from “low” to “high”. The third category of parameters dealt with the time of presence of soundsources such as traffic (T), voices (V), footsteps (F), birds (B), water (Wa) and wind (Wi), from “rarely
present” to “continuously present”.
They treated all the variables as continuous and built multiple linear regression models to predictthe perceived SQ (sound quality) from the other perceptual variables. They obtained:
SQ = 4.48 + 0.52VA – 0.27OL + 0.12V – 0.12T (R 2 adj=0.52)
The results showed that the predicted sound quality explained 52% of the variance of the real
perceived sound quality. A correlation of 0.72 (r=0.72) was obtained between them.
Without visual amenity, they obtained:
SQ = 8.11 − 0.38OL − 0.14T + 0.20V + 0.15B (R 2 =0.34)
Based on the regression method, they found the factors including perceived loudness of global
sound environment and the presence time ratio of certain sound sources (traffic, voices, and birds) that
did not emerge from the background noise significantly influenced the perceived sound quality, andcould be used to predict sound quality in urban context to a certain extent according to the collected
data.
Later, using similar question items on 11-point bipolar semantic scales, Aumond et al (9) collected
the subjective assessments from 37 participants (in four groups) during an urban soundwalk, atdifferent locations along a walk path. Simultaneously, instantaneous 1/3-octave band sound levels andaudio signals were recorded.
Again, they performed multiple linear regression (with stepwise optimization) to model thepleasantness (P) (similar to sound quality above since using the same bipolar semantic scales) using
perceptual parameters. They obtained:
P = 9.70 − 0.47OL − 0.21T + 0.12V + 0.09B (R 2 =0.58)
The predicted pleasantness explains 58% of the pleasantness variance, and 90% (R 2 =0.90) of thepart pleasantness variance due to the change of sound environment (examined by a multilevel
analysis).
Further, they calculated a large set of acoustical indicators from the sound measurements, including
sound pressure level (L), Zwicker loudness (N), dispersion parameters (e.g. L10-L90, N10-N90),
standard deviation of sound pressure level, spectrum centre of gravity, number of noise events,

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normalised time and frequency second derivative (TFSD) (which characterised tonal or harmonicsounds such as voices or birds), and spectral flatness deviation. Then, they proposed multiple linear
regression model to estimate pleasantness based on the most relevant acoustical indicators:
P = 16.48 − 0.25L 50,1kHz + 15.82TFSD mean,500Hz + 16.82TFSD mean,4kHz(1/8s) (R 2 =0.48)
The model explains 48% of the pleasantness variance, and 85% (R 2 =0.85) of the part pleasantness
variance due to the change of sound environment.
4.1.2 Tranquillity
Pheasant et al (10, 11) conducted a series of laboratory studies and used multiple linear regression
to examine the effects of soundscapes and visual features on the perception of tranquillity ofenvironments. They presented audio and visual recordings captured from 11 English rural and urban
landscapes to 44 volunteers in laboratory. Then, they collected the subjects’ subjective assessments ofperceived tranquillity of each location on a 11-point scale, and the perceived loudness of five genericsoundscape components, i.e. human (H), mechanical (M), biological (B), weather (WX), and water(WA), on a 5-point verbal scales (“sound source not present”, “quiet”, “moderately quiet”,“moderately loud”, and “loud”).
By including measured L Aeq , L Amax , L Amin , L A90 , L A10 of the audio recording, the percentage ofvisual natural features (NF) in visual recording, and the perceived loudness of the soundscapecomponents in each location as independent variables, they proposed multiple linear regression
models of tranquillity (TR) as Tranquillity Rating Prediction Tool (TRAPT). Similarly, the perceived
tranquillity on a 11-point scale was treated as a continuous dependent variable.
For the audio only experimental condition (with uni-modal auditory stimuli), the prediction
equations are:TR = 9.99 – 0.93L Amax – 0.45PLM + 1.16PLBorTR = 7.74 – 0.67L Aeq – 0.53PLM + 1.19PLB
where PLM is the perceived loudness of mechanical sounds and PLB is the perceived loudness of
biological sounds.
For the audio-video experimental condition (with bi-modal auditory-visual stimuli), the equationsare:TR = 13.93 − 0.165L Amax + 0.027NF (R 2 =0.52)
or
TR = 8.57 + 0.036NF − 0.11L Aeq (R 2 =0.49)
The results showed that among the factors examined, L Amax or L Aeq , and perceived loudness of
mechanical sounds and biological sounds mostly affected the perceived tranquillity in the audio only
condition, and L Amax or L Aeq , and percentage of visual natural features in the audio-video condition.
4.2 Multinomial Logistic Regression Model
In in-situ questionnaire surveys in green spaces of Cáceres, Spain, Rey Gozalo et al (12) collectedsatisfaction assessments of a random sample of 182 adult visitors. They collected each visitor’s overallsatisfaction with the green spaces, as well as specific satisfactions with the features of cleanliness, air
quality, noise, aesthetics, safety, users, conservation, location, size, groves, and shade, all of whichwere rated on a 5-point Likert scale from “nothing satisfied” to “very satisfied”.
They treated the variables as categorical and used multinomial logistic regression (with stepwise
selection) to study the influence of the specific satisfactions on the overall satisfaction. The likelihood
ratio showed the satisfactions of noise, users, conservation, and shade features contributed
significantly to explaining the overall satisfaction. The regression model generated a McFadden R 2 of
0.41, which was considered to have an excellent fit quality. The model could correctly predict 71.4%of the cases.
4.3 Binomial Logistic Regression Model
Tse et al (13) used binomial logistic regression to predict the acoustic comfort evaluation of urban
parks from multiple factors and investigate the relative impacts of the factors. They conducted in-situ
questionnaire surveys with 595 random users in four public parks in Hong Kong. Sound recordings andsound level measurements were carried out at the survey spots concurrently. They collected users’
responses on subjective perceived sound strength/level (SUB) (“very quiet,” “quiet,” “adequate,”“noisy,” and “very noisy”), acoustic comfort (“very uncomfortable,” “uncomfortable,” “neutral,”“comfortable,” and “very comfortable”) of soundscape, visual comfort of landscape (LAND),6126

preference for natural sounds (PREFN), preference for anthropogenic and mechanical sounds(PREFH) (“very much dislike,” “dislike,” “neutral,” “like,” and “very much like”) on 5-point verbal
scales, and whether they could hear a particular type of sound from a list of sounds (including sounds
from insects (INSECT), bird (BIRD), tree (TREE), water flow (FLOW), wind (WIND), bike (BIKE),
light vehicles (LIGHT), heavy vehicles (HEAVY), talking (TALK), screaming (SCREAM)), as well as
age group (AGE), gender (GENDER), residency status (RESI), duration of stay in a park (DUR), andself-rated auditory sensitivity (AUDIT) (“very bad,” “bad,” “neutral,” “good,” and “very good”). They
also calculated the acoustic indicator of L Aeq (LEQ) from the sound measurements.
Then, to focus on only high or low acoustic comfort evaluation, they dichotomized the variable ofperceived acoustic comfort originally rated on a 5-point verbal scale into binary variable, i.e. “lowacoustic comfort”, referring to a rated response of very uncomfortable, uncomfortable, or neutral, and“high acoustic comfort”, referring to a rated response of comfortable or very comfortable. Other
factors, with an exception of continuous variables such as L Aeq , were also dichotomized in the samemanner. Consequently, they formulated a binomial logit model for predicting the acoustic comfort
evaluation from the multiple factors studied, and then investigated the relative impacts of the factors
through the model.
The results showed a McFadden’s R 2 value of 0.26 for the logit model. Based on the model, bothobjective and subjective sound level, existence of sounds from breeze, bikes, and heavy vehicles,
visual comfort of landscape, residency status, preference for natural sounds, and preference foranthropogenic and mechanical sounds, among the various factors, were found to significantly
influence the acoustic comfort evaluation.

5. SUMMARY
The above research studies show that regression analysis is a useful statistical method to study the
relationship between soundscape effects/descriptors and factors (especially for multiple factors). It
can be used to find the factors that significantly affect the soundscape effects/descriptors from a set of
possible factors and produce models to predict the descriptors given the significant multiple factors.
A number of regression methods are available for analysing different types of dependent variables.
Table 2 gives a summary of the regression methods frequently used for the different dependent
variable types. If a dependent variable is continuous, e.g. a soundscape descriptor rated in a 11-point
scale, multiple linear regression can be used (8-11). If ordinal, e.g. a soundscape descriptor rated in a
5-point scale, ordinal logistic regression can be used. In certain cases, a continuous or ordinal variable,
e.g. a soundscape descriptor rated in a 5-point scale, can be also treated as nominal (12) ordichotomized into binary (13) according to the specific need of research, for which multinomial
logistic regression or binary logistic regression can be used respectively.
Table 2 – Regression methods for different types of dependent variables
ContinuousInterval/ratio
Linear regression
Logistic
regression

Simple linear regression•

Multiple linear regression•

Binary logistic regression
Multinomial logistic regression
Ordinal logistic regression

Categorical
BinaryNominalOrdinal•••ACKNOWLEDGEMENTS
This research is funded by the HEAD-Genuit-Foundation, post-doctoral research fellowshipproject no. P-17/02-W. The author would like to thank Prof. Brigitte Schulte-Fortkamp and Prof.
André Fiebig at TU Berlin, Germany, for the valuable discussions.

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