Models for pedestrian gap acceptance behaviour analysis at unprotected mid-block crosswalks under mixed traffic conditions

Pedestrian safety is an important aspect while crossing the road and it can be explained by pedestrian gap acceptance behaviour. The statistical models such as multiple linear regression (MLR) is often used to model linear relationships between dependent variable (viz., pedestrian gap acceptance behaviour) and independent variables, due to their ability to quantitatively predict the effect of various factors on the dependent variable. However such linear models cannot consider the effect of several variables on the output variable, due to primary assumptions of normality, linear, homoscedasticity and multicollinearity. In this regard, the non-linear models based on the artificial neural network (ANN), which are free from assumptions of linear models, can be easily employed for obtaining the effect of several input variables on the pedestrian accepted gap size. However, researchers have rarely applied ANN modelling technique for predicting the pedestrian gap acceptance behaviour, as the pedestrian gap acceptance behaviour depends on several pedestrian, traffic and vehicular characteristics. The ANN based models would be quite useful in establishing relationship between these factors on the pedestrian gap acceptance behaviour at midblock crosswalks under mixed traffic conditions. In this direction, the present study adopts both MLR as well as ANN with different pedestrian, traffic and vehicular characteristics to assess the significant contributing factors for pedestrians’ gap acceptance behaviour at unprotected mid-block crosswalks under mixed traffic conditions. For this purpose, a video graphic survey was conducted at a six lane divided road at unprotected mid-block crossing in Mumbai, India. The data such as pedestrian (gender and age), vehicular, traffic and pedestrian behavioural characteristics were extracted to model pedestrian accepted gaps. The model results show that pedestrian rolling behaviour has a significant effect on pedestrian accepted gap size. The model results concluded that ANN has a better prediction with possibility to consider the effect of more number of variables on the pedestrian gap acceptance behaviour as compared to the MLR model under mixed traffic conditions. However, the quantification of significant contributing variables on pedestrian accepted gap size is easy by MLR model as compared to the ANN technique. So, both models have their own significant role in pedestrian gap acceptance analysis. The developed models may be useful to enhance the existing mid-block crosswalk facilities or planning new facilities by more accurate prediction of the pedestrian gap acceptance behaviour considering the influence of various factors under mixed traffic conditions.     

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

In recent years, network models have been proposed as an alternative representation of psychometric constructs such as depression. In such models, the covariance between observables (e.g., symptoms like depressed mood, feelings of worthlessness, and guilt) is explained in terms of a pattern of causal interactions between these observables, which contrasts with classical interpretations in which the observables are conceptualized as the effects of a reflective latent variable. However, few investigations have been directed at the question how these different models relate to each other. To shed light on this issue, the current paper explores the relation between one of the most important network models—the Ising model from physics—and one of the most important latent variable models—the Item Response Theory (IRT) model from psychometrics. The Ising model describes the interaction between states of particles that are connected in a network, whereas the IRT model describes the probability distribution associated with item responses in a psychometric test as a function of a latent variable. Despite the divergent backgrounds of the models, we show a broad equivalence between them and also illustrate several opportunities that arise from this connection.     

Generalized latent variable models with non‐linear effects

Until recently, item response models such as the factor analysis model for metric responses, the two‐parameter logistic model for binary responses and the multinomial model for nominal responses considered only the main effects of latent variables without allowing for interaction or polynomial latent variable effects. However, non‐linear relationships among the latent variables might be necessary in real applications. Methods for fitting models with non‐linear latent terms have been developed mainly under the structural equation modelling approach. In this paper, we consider a latent variable model framework for mixed responses (metric and categorical) that allows inclusion of both non‐linear latent and covariate effects. The model parameters are estimated using full maximum likelihood based on a hybrid integration–maximization algorithm. Finally, a method for obtaining factor scores based on multiple imputation is proposed here for the non‐linear model.     

Exploratory regression analysis: A tool for selecting models and determining predictor importance

Linear regression analysis is one of the most important tools in a researcher’s toolbox for creating and testing predictive models. Although linear regression analysis indicates how strongly a set of predictor variables, taken together, will predict a relevant criterion (i.e., the multiple R), the analysis cannot indicate which predictors are the most important. Although there is no definitive or unambiguous method for establishing predictor variable importance, there are several accepted methods. This article reviews those methods for establishing predictor importance and provides a program (in Excel) for implementing them (available for direct download at . The program investigates all 2 ^p – 1 submodels and produces several indices of predictor importance. This exploratory approach to linear regression, similar to other exploratory data analysis techniques, has the potential to yield both theoretical and practical benefits.     

基于多元回归的调节效应分析

在心理学和其他社科研究领域,大量实证研究建立调节模型,以分析自变量对因变量关系的影响机制,但在基于多元回归的调节效应分析实践中仍存在不足。我们回顾了均值中心化在基于多元回归的调节效应分析中的作用,均值中心化不影响乘积项(即调节效应)的检验,仅对一阶项(即主效应)的检验有影响。讨论了简单斜率的检验方法,建议在调节变量为连续变量时,使用Johnson-Neyman法进行简单斜率检验;在调节变量为类别变量或研究者对某个调节变量值感兴趣时,使用选点法。并用一个实际例子演示如何进行调节效应分析。随后展望了调节效应检验的拓展方向。     

Binary recursive partitioning: Background,methods, and application to psychology

Binary recursive partitioning (BRP) is a computationally intensive statistical method that can be used in situations where linear models are often used. Instead of imposing many assumptions to arrive at a tractable statistical model, BRP simply seeks to accurately predict a response variable based on values of predictor variables. The method outputs a decision tree depicting the predictor variables that were related to the response variable, along with the nature of the variables' relationships. No significance tests are involved, and the tree's ‘goodness’ is judged based on its predictive accuracy. In this paper, we describe BRP methods in a detailed manner and illustrate their use in psychological research. We also provide R code for carrying out the methods.     

Strategic aspects of numerosity judgment: the effect of task characteristics

In previous investigations we documented that people use several strategies to determine different numerosities of blocks that are presented in a square grid. One of these strategies is the clever subtraction strategy, wherein the number of empty squares in the grid is subtracted from the total number of squares in the grid. In the present study we investigated participants' flexibility in strategy use when varying the shape of the grid. Analysis of the results in terms of the theoretical framework of Lemaire and Siegler (1995) regarding strategic change shows that this contextual variable affected the frequency, execution time, and accuracy of subjects' use of the subtraction strategy. The usefulness of this framework for analyzing the nature of the adaptation to contextual variations is discussed. From a methodological point of view, this study documents the potential of Beem's (1993, 1999) segmented linear regression models for assessing subjects' strategy use in cognitive tasks.     

Using statistical smoothing to estimate the psycholinguistic acceptability of novel phrases

Native speakers of languages perceive differences in the acceptability of phrases even when those phrases are both grammatical and novel (previously unseen). We suggest that smoothing, a statistical technique used by natural language processing engineers, provides several candidate mechanisms for investigating this phenomenon. We describe the creation of a large data set of predictions from several smoothing algorithms about the acceptability of unseen grammatical phrases and a novel experimental method for the pairwise comparison of these models. We use this method to compare three smoothing methods and consider the results in light of the differences among the models. We argue that the data support the idea that similarity in this domain is best thought of as a form of asymmetric representational distortion and that the informational basis over which such estimates are made is broad, rather than narrow, as has been previously suggested.     

A comparison of methods for estimating quadratic effects in nonlinear structural equation models

Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent moderated structural equation method, (d) a fully Bayesian approach, and (e) marginal maximum likelihood estimation. Of the 5 estimation methods, it was found that overall the methods based on maximum likelihood estimation and the Bayesian approach performed best in terms of bias, root-mean-square error, standard error ratios, power, and Type I error control, although key differences were observed. Similarities as well as disparities among methods are highlight and general recommendations articulated. As a point of comparison, all 5 approaches were fit to a reparameterized version of the latent quadratic model to educational reading data.     

Linearity of Personality–Performance Relationships: A large‐scale examination

This paper reviews theory and past research concerning nonlinear relationships between personality tests and job performance. We compare linear and nonlinear regression models for each of the 32 Occupational Personality Questionnaire (OPQ32i) scales using job performance as the criterion variable. We evaluate linear, quadratic, and cubic relationships between personality and job performance by calculating changes in R (ΔR) between the linear and nonlinear models. We use 3 decision rules of varying levels for ΔR and divide a large sample randomly into 2 samples to cross‐validate any nonlinear effects found. Few scales exhibited nonlinearity and the magnitude of the departures from linearity were small.     

A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the metropolis-hastings algorithm

Nonlinear latent variable models are specified that include quadratic forms and interactions of latent regressor variables as special cases. To estimate the parameters, the models are put in a Bayesian framework with conjugate priors for the parameters. The posterior distributions of the parameters and the latent variables are estimated using Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis-Hastings algorithm. The proposed estimation methods are illustrated by two simulation studies and by the estimation of a non-linear model for the dependence of performance on task complexity and goal specificity using empirical data.     

Time-specific Errors in Growth Curve Modeling: Type-1 Error Inflation and a Possible Solution with Mixed-Effects Models

Growth curve modeling (GCM) has been one of the most popular statistical methods to examine participants’ growth trajectories using longitudinal data. In spite of the popularity of GCM, little attention has been paid to the possible influence of time-specific errors, which influence all participants at each timepoint. In this article, we demonstrate that the failure to take into account such time-specific errors in GCM produces considerable inflation of type-1 error rates in statistical tests of fixed effects (e.g., coefficients for the linear and quadratic terms). We propose a GCM that appropriately incorporates time-specific errors using mixed-effects models to address the problem. We also provide an applied example to illustrate that GCM with and without time-specific errors would lead to different substantive conclusions about the true growth trajectories. Comparisons with other models in longitudinal data analysis and potential issues of model misspecification are discussed.     

两类常见的类别变量调节效应分析

类别变量在心理学和其他社科研究领域经常遇到,当自变量或调节变量为类别变量时,应当如何分析调节效应呢？详述了多类别变量的被试间设计和两水平被试内设计（因变量重复测量2次）的调节效应分析方法,并给出了分析流程。先进行调节效应的显著性检验,后用选点法或Johnson-Neyman法进行简单斜率检验。多类别变量被试间设计的简单斜率检验是先进行整体检验,后进行配对检验。用两个实际例子演示如何进行类别变量的调节效应分析,最后展望了两类设计的类别变量调节研究的拓展方向,例如更复杂的类别变量的调节模型等。     

Flexibility in strategy use: Adaptation of numerosity judgement strategies to task characteristics

In previous investigations we documented that people use several strategies to determine numerosities of blocks that are presented in a square grid. One of these strategies is the clever subtraction strategy, wherein the number of empty squares in the grid is subtracted from the total number of squares in the grid. In the present study we investigated participants' flexibility in strategy use when varying the size of the grids. Results are described in terms of the theoretical framework of Lemaire and Siegler (1995) regarding strategic change, and show that this contextual variable affected the frequency, execution time, and accuracy of subjects' use of the subtraction strategy. The usefulness of this framework for analysing the nature of the adaptation to contextual variations is discussed. From a methodological point of view, this study documents the potential of Beem's (1993, 1999) segmented linear regression models for assessing subjects' strategy use in cognitive tasks.     

Heuristic and linear models of judgment: matching rules and environments

Much research has highlighted incoherent implications of judgmental heuristics, yet other findings have demonstrated high correspondence between predictions and outcomes. At the same time, judgment has been well modeled in the form of as if linear models. Accepting the probabilistic nature of the environment, the authors use statistical tools to model how the performance of heuristic rules varies as a function of environmental characteristics. They further characterize the human use of linear models by exploring effects of different levels of cognitive ability. They illustrate with both theoretical analyses and simulations. Results are linked to the empirical literature by a meta-analysis of lens model studies. Using the same tasks, the authors estimate the performance of both heuristics and humans where the latter are assumed to use linear models. Their results emphasize that judgmental accuracy depends on matching characteristics of rules and environments and highlight the trade-off between using linear models and heuristics. Whereas the former can be cognitively demanding, the latter are simple to implement. However, heuristics require knowledge to indicate when they should be used.     

Beyond Empirical Adequacy: Learning Progressions as Models and Their Value for Teachers

As scientific models of student thinking, learning progressions (LPs) have been evaluated in terms of one important, but limited, criterion: fit to empirical data. We argue that LPs are not empirically adequate, largely because they rely on problematic assumptions of theory-like coherence in students’ thinking. Through an empirical investigation of physics teachers’ interactions with an LP-based score report, we investigate 2 other criteria of good models: utility and generativity. When interacting with LP-based materials, teachers often adopted finer-grained perspectives (in contrast to the levels-based perspective of the LP itself) and used these finer-grained perspectives to formulate more specific, actionable instructional ideas than when they reasoned in terms of LP levels. However, although teachers did not use the LP-based materials in ways envisioned by LP researchers, the teachers’ interactions with the score reports embodied how philosophers envision the fruitful use of good models of dynamic, complex systems. In particular, teachers took a skeptical, inquiring stance toward the LP, using it as an oversimplified starting place for generating and testing hypotheses about student thinking and using concepts from the model in ways that moved beyond the knowledge available in the LP. Thus, despite—and perhaps even because of—their empirical inadequacy, LPs have the potential to serve teachers as productive models in ways not envisioned by LP researchers: as tools for knowledge generation.     

SPSS macros to compare any two fitted values from a regression model

In regression models with first-order terms only, the coefficient for a given variable is typically interpreted as the change in the fitted value of Y for a one-unit increase in that variable, with all other variables held constant. Therefore, each regression coefficient represents the difference between two fitted values of Y. But the coefficients represent only a fraction of the possible fitted value comparisons that might be of interest to researchers. For many fitted value comparisons that are not captured by any of the regression coefficients, common statistical software packages do not provide the standard errors needed to compute confidence intervals or carry out statistical tests—particularly in more complex models that include interactions, polynomial terms, or regression splines. We describe two SPSS macros that implement a matrix algebra method for comparing any two fitted values from a regression model. The !OLScomp and !MLEcomp macros are for use with models fitted via ordinary least squares and maximum likelihood estimation, respectively. The output from the macros includes the standard error of the difference between the two fitted values, a 95% confidence interval for the difference, and a corresponding statistical test with its p-value.     

Partial analysis of high-way factorial designs

Inclusion of several variables in a design is often desirable, but each added variable doubles the number of significance tests in the routine analysis of variance. This note discusses a procedure of partial analysis in which interactions, primarily those involving minor variables, are omitted from the analysis when prior evidence indicates that they are probably negligible. The rationale of this procedure is given, and its use illustrated in a model experiment. Specific recommendations for handling systematic sources and error terms are given.