An adaptive approach for modelling multiattribute choice

An adaptive approach for modelling individual-level choice among multiattribute alternatives using the binary logit model is presented. The algorithm involves the collection of paired comparison data. In an effort to maximize the amount of information obtainable from each response, it is based on the experimental design criterion of D-optimality. A simulation study indicates that the proposed algorithm outperforms other sequential selection approaches in terms of estimation accuracy and predictive efficiency under certain circumstances. The results appear to encourage the use of such an adaptive algorithm for individual-level modelling in light of the potential reduction in data requirements without significant loss in predictive accuracy.     

Analysis of multivariate mixed longitudinal data: A flexible latent process approach

Multivariate ordinal and quantitative longitudinal data measuring the same latent construct are frequently collected in psychology. We propose an approach to describe change over time of the latent process underlying multiple longitudinal outcomes of different types (binary, ordinal, quantitative). By relying on random‐effect models, this approach handles individually varying and outcome‐specific measurement times. A linear mixed model describes the latent process trajectory while equations of observation combine outcome‐specific threshold models for binary or ordinal outcomes and models based on flexible parameterized non‐linear families of transformations for Gaussian and non‐Gaussian quantitative outcomes. As models assuming continuous distributions may be also used with discrete outcomes, we propose likelihood and information criteria for discrete data to compare the goodness of fit of models assuming either a continuous or a discrete distribution for discrete data. Two analyses of the repeated measures of the Mini‐Mental State Examination, a 20‐item psychometric test, illustrate the method. First, we highlight the usefulness of parameterized non‐linear transformations by comparing different flexible families of transformation for modelling the test as a sum score. Then, change over time of the latent construct underlying directly the 20 items is described using two‐parameter longitudinal item response models that are specific cases of the approach.     

Estimation of nonlinear mixed-effects continuous-time models using the continuous-discrete extended Kalman filter

Many intensive longitudinal measurements are collected at irregularly spaced time intervals, and involve complex, possibly nonlinear and heterogeneous patterns of change. Effective modelling of such change processes requires continuous-time differential equation models that may be nonlinear and include mixed effects in the parameters. One approach of fitting such models is to define random effect variables as additional latent variables in a stochastic differential equation (SDE) model of choice, and use estimation algorithms designed for fitting SDE models, such as the continuous-discrete extended Kalman filter (CDEKF) approach implemented in the dynr R package, to estimate the random effect variables as latent variables. However, this approach's efficacy and identification constraints in handling mixed-effects SDE models have not been investigated. In the current study, we analytically inspect the identification constraints of using the CDEKF approach to fit nonlinear mixed-effects SDE models; extend a published model of emotions to a nonlinear mixed-effects SDE model as an example, and fit it to a set of irregularly spaced ecological momentary assessment data; and evaluate the feasibility of the proposed approach to fit the model through a Monte Carlo simulation study. Results show that the proposed approach produces reasonable parameter and standard error estimates when some identification constraint is met. We address the effects of sample size, process noise variance, and data spacing conditions on estimation results.     

Recursive Partitioning with Nonlinear Models of Change

In this article, we introduce nonlinear longitudinal recursive partitioning (nLRP) and the R package longRpart2 to carry out the analysis. This method implements recursive partitioning (also known as decision trees) in order to split data based on individual- (i.e., cluster) level covariates with the goal of predicting differences in nonlinear longitudinal trajectories. At each node, a user-specified linear or nonlinear mixed-effects model is estimated. This method is an extension of Abdolell et al.'s (2002) longitudinal recursive partitioning while permitting a nonlinear mixed-effects model in addition to a linear mixed-effects model in each node. We give an overview of recursive partitioning, nonlinear mixed-effects models for longitudinal data, describe nLRP, and illustrate its use with empirical data from the Early Childhood Longitudinal Study—Kindergarten Cohort.     

An Examination of a Functional Mixed-Effects Modeling Approach to the Analysis of Longitudinal Data

Growth curve modeling is one of the main analytical approaches to study change over time. Growth curve models are commonly estimated in the linear and nonlinear mixed-effects modeling framework in which both the mean and person-specific curves are modeled parametrically with functions of time such as the linear, quadratic, and exponential. However, when more complex nonlinear trajectories need to be estimated and researchers do not have a priori knowledge of an appropriate functional form of growth, parametric models may be too restrictive. This paper reviews functional mixed-effects models, a nonparametric extension of mixed-effects models that permit both the mean and person-specific curves to be estimated without assuming a prespecified functional form of growth. Details of the model are presented along with results from a simulation study and an empirical example. The simulation study showed functional mixed-effects models performed reasonably well under various conditions commonly associated with longitudinal panel data, such as few time points per person, irregularly spaced time points across persons, missingness, and nonlinear trajectories. The usefulness of functional mixed-effects models is illustrated by analyzing empirical data from the Early Childhood Longitudinal Study – Kindergarten Class of 1998–1999.     

Decision ecology: Foraging and the ecology of animal decision making

In this article, I review the approach taken by behavioral ecologists to the study of animal foraging behavior and explore connections with general analyses of decision making. I use the example of patch exploitation decisions in this article in order to develop several key points about the properties of naturally occurring foraging decisions. First, I argue that experimental preparations based on binary, mutually exclusive choice are not good models of foraging decisions. Instead, foraging choices have a sequential foreground-background structure, in which one option is in the background of all other options. Second, behavioral ecologists view foraging as a hierarchy of decisions that range from habitat selection to food choice. Finally, data suggest that foraging animals are sensitive to several important trade-offs. These trade-offs include the effects of competitors and group mates, as well as the problem of predator avoidance.     

Conditional mixed models with crossed random effects

The analysis of continuous hierarchical data such as repeated measures or data from meta‐analyses can be carried out by means of the linear mixed‐effects model. However, in some situations this model, in its standard form, does pose computational problems. For example, when dealing with crossed random‐effects models, the estimation of the variance components becomes a non‐trivial task if only one observation is available for each cross‐classified level. Pseudolikelihood ideas have been used in the context of binary data with standard generalized linear multilevel models. However, even in this case the problem of the estimation of the variance remains non‐trivial. In this paper, we first propose a method to fit a crossed random‐effects model with two levels and continuous outcomes, borrowing ideas from conditional linear mixed‐effects model theory. We also propose a crossed random‐effects model for binary data combining ideas of conditional logistic regression with pseudolikelihood estimation. We apply this method to a case study with data coming from the field of psychometrics and study a series of items (responses) crossed with participants. A simulation study assesses the operational characteristics of the method.     

Fitting multilevel models with ordinal outcomes: performance of alternative specifications and methods of estimation

Previous research has compared methods of estimation for fitting multilevel models to binary data, but there are reasons to believe that the results will not always generalize to the ordinal case. This article thus evaluates (a) whether and when fitting multilevel linear models to ordinal outcome data is justified and (b) which estimator to employ when instead fitting multilevel cumulative logit models to ordinal data, maximum likelihood (ML), or penalized quasi-likelihood (PQL). ML and PQL are compared across variations in sample size, magnitude of variance components, number of outcome categories, and distribution shape. Fitting a multilevel linear model to ordinal outcomes is shown to be inferior in virtually all circumstances. PQL performance improves markedly with the number of ordinal categories, regardless of distribution shape. In contrast to binary data, PQL often performs as well as ML when used with ordinal data. Further, the performance of PQL is typically superior to ML when the data include a small to moderate number of clusters (i.e., ≤ 50 clusters).     

Hidden patterns of play interaction in soccer using SOF-CODER

Traditional methods for quantifying sport performances are limited in their capacity to describe the complex interactions of events that occur within a performance over time. The following article outlines a new approach to the study of actions between players in team sports—mainly, soccer. Since the observational design is nomothetic, point, and multidimensional, an observational and data-collecting instrument has been developed. The instrument is mixed and combines a field format with a category system for game events, as well as an ad hoc instrument that considers the game actions of one or both teams, each recorded according to the same criteria. The article also outlines a new approach to the analysis of time-based event records—in this case, sports performance—known as T-pattern detection. The relevant elements of the T-pattern detection process are explained, and exemplar data from analyses of soccer matches are presented to highlight the potential of this form of data analysis. The results suggest that it is possible to identify new kinds of profiles for both individuals and teams on the basis of observational criteria and a further analysis of temporal behavioral patterns detected within the performances.     

Validating Cultureand Gender-Specific Constructs

SUMMARY

Despite on-going calls for developing cultural competency among mental health practitioners, few assessment instruments consider cultural variation in psychological constructs. To meet the challenge of developing measures for minority and international students, it is necessary to account for the influence culture may have on the latent constructs that form a given instrument. What complicates matters further is that individual factors (e.g., gender) within a culture necessitate additional refinement of factor structures on which such instruments are based. The current work endeavors to address these concerns by demonstrating a mixed-methods approach utilized to assess construct validation within a specific culture; and in turn develop culturally-specific instruments. Qualitative methods were used to inform the development of a structured self-report by gaining detailed knowledge of the target culture and creating items grounded in interview and observational data. Factor analysis techniques and triangulation with qualitative analyses validated these findings. Previous work (Sarkar, 2003) suggested a number of gender-specific perceptions of mental health constructs within the target culture and these were investigated using additional mixed-method analyses. This article demonstrates an emerging mixed-method technique for developing culturally sound assessment tools, offers guidance on how to incorporate the overall approach in assessment, and provides a basis for thinking critically about the use of existing instruments when working with diverse populations.     

Marital research in the 20th century and a research agenda for the 21st century

In this article we review the advances made in the 20th century in studying marriages. Progress moved from a self-report, personality-based approach to the study of interaction in the 1950s, following the advent of general systems theory. This shift led, beginning in the 1970s, to the rapid development of marital research using a multimethod approach. The development of more sophisticated observational measures in the 1970s followed theorizing about family process that was begun in the decade of the 1950s. New techniques for observation, particularly the study of affect and the merging of synchronized data streams using observational and self-report perceptual data, and the use of sequential and time-series analyses produced new understandings of process and power. Research in the decades of the 1980s and 1990s witnessed the realization of many secular changes in the American family, including the changing role of women, social science's discovery of violence and incest in the family, the beginning of the study of cultural variation in marriages, the expansion of the measurement of marital outcomes to include longevity, health, and physiology (including the immune system), and the study of comorbidities that accompany marital distress. A research agenda for the 21st century is then described.     

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.     

Back to Basics with Mixed-Effects Models: Nine Take-Away Points

Purpose

Multilevel mixed effects models are widely used in organizational behavior and organizational psychology to test and advance theory. At times, however, the complexity of the models leads researchers to draw erroneous inferences or otherwise use the models in less than optimal ways. We present nine take-away points intended to enhance the theoretical precision and utility of the models.

Approach

We demonstrate our points using two types of simulated data: one in which group membership is irrelevant, and the other in which relationships exist only because of group membership. We then demonstrate that the effects we observe in simulated data replicate in organizational data.

Findings

Little that we address will be new to methodology experts; nonetheless, we draw together a variety of points that we believe will help advance both theory and analytic rigor in multilevel analyses.

Implications

We make two points that run somewhat counter to conventional norms. First, we argue that mixed-effects models are appropriate even when ICC(1) values associated with the outcome data are small and non-significant. Second, we show that high ICC(2) values are not a prerequisite for detecting emergent multilevel relationships.

Originality/Value

The article is designed to be a resource for researchers who are learning about and applying mixed-effects (i.e., multilevel) models.

     

二分数据的多层线性模型:原理与应用

分类数据的多层线性模型在我国的心理学研究中鲜有使用。本研究旨在将这种模型引入到我国心理学研究之中。论文首先介绍了二分数据的多层线性模型的原理和假设条件、参数估计和假设检验,然后以6187名小学生为被试,采用二分变量的多层线性模型,说明了个体因素和学校因素对儿童攻击行为的影响,并对分析结果进行了解释。     

A Note on Comparing the Estimates of Models for Cluster-Correlated or Longitudinal Data with Binary or Ordinal Outcomes

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for binary or ordered-categorical outcomes, however, comparisons between such models are impeded by the implicit rescaling of the model estimates that takes place with the inclusion of new predictors and/or random effects. This paper presents an approach for putting the estimates on a common scale to facilitate relative comparisons between models fit to binary or ordinal outcomes. The approach is developed for both population-average and unit-specific models.     

A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables

Uncorrectable skew and heteroscedasticity are among the "lemons" of psychological data, yet many important variables naturally exhibit these properties. For scales with a lower and upper bound, a suitable candidate for models is the beta distribution, which is very flexible and models skew quite well. The authors present maximum-likelihood regression models assuming that the dependent variable is conditionally beta distributed rather than Gaussian. The approach models both means (location) and variances (dispersion) with their own distinct sets of predictors (continuous and/or categorical), thereby modeling heteroscedasticity. The location sub-model link function is the logit and thereby analogous to logistic regression, whereas the dispersion sub-model is log linear. Real examples show that these models handle the independent observations case readily. The article discusses comparisons between beta regression and alternative techniques, model selection and interpretation, practical estimation, and software.     

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.     

Using generalized additive (mixed) models to analyze single case designs

This article shows how to apply generalized additive models and generalized additive mixed models to single-case design data. These models excel at detecting the functional form between two variables (often called trend), that is, whether trend exists, and if it does, what its shape is (e.g., linear and nonlinear). In many respects, however, these models are also an ideal vehicle for analyzing single-case designs because they can consider level, trend, variability, overlap, immediacy of effect, and phase consistency that single-case design researchers examine when interpreting a functional relation. We show how these models can be implemented in a wide variety of ways to test whether treatment is effective, whether cases differ from each other, whether treatment effects vary over cases, and whether trend varies over cases. We illustrate diagnostic statistics and graphs, and we discuss overdispersion of data in detail, with examples of quasibinomial models for overdispersed data, including how to compute dispersion and quasi-AIC fit indices in generalized additive models. We show how generalized additive mixed models can be used to estimate autoregressive models and random effects and discuss the limitations of the mixed models compared to generalized additive models. We provide extensive annotated syntax for doing all these analyses in the free computer program R.     

Dyadic peer interaction and task orientation in attention-deficit-disordered children

A sequential observational approach was used to compare peer interactions in 10 mixed dyads of ADD-H and non-Add-H boys and 10 dyads of non-ADD-H boys in laboratory cooperative and school classroom task analogue activities. Mixed dyads were found to have a greater frequency of aggression and less joint activity than control dyads in specific situations. No differences were found for measures of functional attention as measured by frequency, duration, and mean duration of task-oriented behavior. Lag sequential analyses revealed two major sequences that differentiated mixed from normal dyads. These were Verbal Reciprocity (a measure of reciprocal verbal interaction) and Retreat (a measure of social withdrawal following aggression).