Robustness of expected utility model in predicting individual choices

In this paper we show how utility, lottery dependent utility, and weighted utility models can be calibrated using algebraic and statistical techniques. The models are empirically compared in laboratory (student subjects) and real settings (sales force personnel of the Los Angeles Times). In our empirical comparison we evaluate two aspects: the extent to which observed preferences are consistent with each model, and predictive accuracy of the models on a holdout sample. The results indicate that only about 20% of the observed choice patterns in our experimental design are consistent with the expected utility model, 50% with the weighted utility model, and 90% with the general lottery dependent utility model. On individual level predictions to the holdout sample, however, the expected utility model does as well as the other two models. This latter finding is robust across different measurement and estimation methods and student and non-student subjects.     

Fitting Psychometric Models with Methods Based on Automatic Differentiation

Quantitative psychology is concerned with the development and application of mathematical models in the behavioral sciences. Over time, models have become more complex, a consequence of the increasing complexity of research designs and experimental data, which is also a consequence of the utility of mathematical models in the science. As models have become more elaborate, the problems of estimating them have become increasingly challenging. This paper gives an introduction to a computing tool called automatic differentiation that is useful in calculating derivatives needed to estimate a model. As its name implies, automatic differentiation works in a routine way to produce derivatives accurately and quickly. Because so many features of model development require derivatives, the method has considerable potential in psychometric work. This paper reviews several examples to demonstrate how the methodology can be applied. From the Presidential Address delivered at the 70th Annual Meeting of the Psychometric Society, Tilburg University, The Netherlands, July 5–8, 2005.     

Additivity and expected utility in risky multiattribute preferences

This experiment analyzed human preferences among even chance gambles for commodity bundles. The purpose of the experiment was to test several independence assumptions that distinguish between models for risky multiattribute preferences. In particular, the additivity and the expected utility part of the additive expected utility model were tested symmetrically. The degree and form of model violations were established, and the effects of instructions and of response modes were examined. All independence assumptions were violated by a bias to prefer a gamble or a commodity bundle that was previously matched against a standard. Systematic and strong violations that superseded this bias questioned the validity of the additive expected utility model. In violation of the additivity part of that model subjects consistently preferred the gamble with more balanced outcomes when comparing gambles with identical marginal probability distributions. This trend, called multiattribute risk aversion, was independent of subjects' single attribute risk attitude. Instructions and response modes had no noticeable impacts on these response patterns.     

The order-restricted association model: Two estimation algorithms and issues in testing

This paper presents a row-column (RC) association model in which the estimated row and column scores are forced to be in agreement with an a priori specified ordering. Two efficient algorithms for finding the order-restricted maximum likelihood (ML) estimates are proposed and their reliability under different degrees of association is investigated by a simulation study. We propose testing order-restricted RC models using a parametric bootstrap procedure, which turns out to yield reliablep values, except for situations in which the association between the two variables is very weak. The use of order-restricted RC models is illustrated by means of an empirical example. Francisca Galindo performed this research as a part of her PhD. dissertation project at Tilburg University.     

A note on structural models for the circumplex

Jöreskog (1974) developed a latent variable model for the covariance structure of the circumplex which, under certain conditions, includes a model for a patterned correlation matrix (Browne, 1977). This model is of limited usefulness, however, in that it employs a known matrix that is rank deficient for many problems. Furthermore, the model is inappropriate for the circumplex which contains negative covariances. This paper presents alternative models for the perfect circumplex and quasi-circumplex that avoids these difficulties, and that includes the important model for a patterned correlation circumplex matrix. Two numerical examples are provided.This research was supported in part by a grant from the Graduate School of the University of Minnesota. I wish to thank M. W. Browne for suggesting the final model presented in this paper. James Steiger and the Editor also made several valuable suggestions.     

J scale models for preference behavior

Three models for preference behavior are developed within the framework of Coombs' theory of data, an absolute difference model, a ratio model, and a two-stage model. Each of these models describes a mechanism by which unilateral preferences may be determined on a unidimensionalJ scale. Differential implications of the models for response latencies are derived, and some early data employing an application of the unfolding technique are presented in support of the two-stage model.Based upon portions of the author's doctoral dissertation, University of Michigan, 1962. This research was supported in part by NSF Grant No. G5820 to Professor C. H. Coombs. The writer also wishes to thank Professor William Hays, who served as committee chairman and offered considerable support and assistance.     

Matrix analysis of identifiability of some finite markov models

Methods developed by Bernbach [1966] and Millward [1969] permit increased generality in analyses of identifiability. Matrix equations are presented that solve part of the identifiability problem for a class of Markov models. Results of several earlier analyses are shown to involve special cases of the equations developed here. And it is shown that a general four-state chain has the same parameter space as an all-or-none model if and only if its representation with an observable absorbing state is lumpable into a Markov chain with three states.This research was supported by the U.S. Public Health Service under Grant MH-12717 to Indiana University and Grant GM-1231 to the University of Michigan.Now at the University of Texas, Austin.     

The use of limit theorems in paired comparison model building

The Thurstone and the Bradley-Terry models, both initially advanced on intuitive grounds, have proved useful in the analysis of paired comparisons. The psychological meaning of these models and their relation to one another is unclear, but they fit data. Stevens has observed that there may be two basic mechanisms of discrimination 1) additive and 2) substitutive. We advance two corresponding mathematical models: that experienced sensation is 1) the sum of a large number of independent signals and 2) the maximum of a large number of independent signals. These assumptions yield 1) Thurstone's model and 2) the model of Bradley-Terry. Psychological interpretations of the various parameters, in terms of sensation, present themselves in a natural manner. Thus this paper presents a theory which unifies and interprets two paired comparison models that have proved useful in fitting experimental data.This research was supported in part by a National Science Foundation Grant GP 3807 and by the Army, Navy, and Air Force under ONR Contract # NONR-988(08), Task Order NR 042-004 with the Florida State University.     

Discrete Choice Models for Ordinal Response Variables: A Generalization of the Stereotype Model

In this paper I present a class of discrete choice models for ordinal response variables based on a generalization of the stereotype model. The stereotype model can be derived and generalized as a random utility model for ordered alternatives. Random utility models can be specified to account for heteroscedastic and correlated utilities. In the case of the generalized stereotype model this includes category-specific random effects due to individual differences in response style. But unlike standard random utility models the generalized stereotype model is better suited for ordinal response variables and can be interpreted as a kind of unidimensional unfolding model. This paper discusses the specification, interpretation, identification, and estimation of generalized stereotype models. Two applications are provided for illustration. This paper benefited significantly from the comments and suggestions of the editor, associate editor, and three anonymous reviewers. It is dedicated to my late colleague, peer, and friend Bradley D. Crouch.     

Parent involvement,expectancy values,and STEM outcomes among underrepresented adolescents

Racial and ethnic achievement gaps contribute to the lack of underrepresented minorities in STEM-related careers. This research is grounded in the expectancy-value model of achievement motivation which posits that motivation is influenced by social-cognitive variables such as self-efficacy and beliefs about the usefulness or utility of the task. These social-cognitive variables (self-beliefs and task beliefs), in turn, are influenced by numerous ecological factors such as parental involvement. Parent involvement can promote children’s self-efficacy and task beliefs which is important for STEM interest and persistence. This study utilized data from the High School Longitudinal Study: 2009 (HLS: 2009) to examine links among parent involvement and underrepresented students’ STEM self-efficacy, utility, interest and achievement. Concurrent and longitudinal models conducted in MPlus tested whether parent involvement in 9th grade predicted STEM interest and achievement directly and indirectly via self-efficacy and utility. Concurrent models showed that parent involvement in STEM was significantly related to adolescents’ STEM self-efficacy which in turn was significantly related to STEM interest and achievement. Longitudinal models showed that parents’ STEM involvement in 9th grade predicted adolescents’ STEM efficacy in 11th grade which in turn predicted adolescents’ cumulative GPA in STEM courses. Parent involvement in STEM was more strongly and consistently linked to self-efficacy than to utility. These results suggest that parent involvement in STEM helps adolescents to feel more confident in their STEM abilities but it does not necessarily contribute to adolescents’ STEM utility values.

     

A Latent Transition Model With Logistic Regression

Latent transition models increasingly include covariates that predict prevalence of latent classes at a given time or transition rates among classes over time. In many situations, the covariate of interest may be latent. This paper describes an approach for handling both manifest and latent covariates in a latent transition model. A Bayesian approach via Markov chain Monte Carlo (MCMC) is employed in order to achieve more robust estimates. A case example illustrating the model is provided using data on academic beliefs and achievement in a low-income sample of adolescents in the United States. This research was partially supported by the National Institute on Drug Abuse Grant 1-R03-DA021639. This research was partially supported by the National Institute on Drug Abuse Grant 1-P50-DA10075, The Methodology Center, The Pennsylvania State University. This research was partially supported by the National Institute of Mental Health funds as part of the Studying Diverse Lives research support program at the Henry A. Murray Research Archive, Institute for Quantitative Science, Harvard University.     

Some results on random utility models

This paper extends earlier work on the properties of Thurstone choice models to the general random utility model (RUM), in which the components of the random utility vector are not necessarily independent and identically distributed, even apart from location shifts. The condition for two RUMs to be equivalent is established, and relationships between the choice axiom, decomposition, and other conditions are explored. In the special case of the Thurstone model, the conditions considered are all equivalent to the double exponential distribution.     

Regime-Switching Bivariate Dual Change Score Model

Mixture structural equation model with regime switching (MSEM-RS) provides one possible way of representing over-time heterogeneities in dynamic processes by allowing a system to manifest qualitatively or quantitatively distinct change processes conditional on the latent “regime” the system is in at a particular time point. Unlike standard mixture structural equation models such as growth mixture models, MSEM-RS allows individuals to transition between latent classes over time. This class of models, often referred to as regime-switching models in the time series and econometric applications, can be specified as regime-switching mixture structural equation models when the number of repeated measures involved is not large. We illustrate the empirical utility of such models using one special case—a regime-switching bivariate dual change score model in which two growth processes are allowed to manifest regime-dependent coupling relations with one another. The proposed model is illustrated using a set of longitudinal reading and arithmetic performance data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 study (ECLS-K; U.S. Department of Education, National Center for Education Statistics, 2010).     

Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm

Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an EM algorithm are used. By characterizing the ability distribution empirically, arbitrary assumptions about its form are avoided. The Em procedure is shown to apply to general item-response models lacking simple sufficient statistics for ability. This includes models with more than one latent dimension.Supported in part by NSF grant BNS 7912417 to the University of Chicago and by SSRC (UK) grant HR6132 to the University of Lancaster.We are indebted to Mark Reiser and Robert Gibbons for computer programming. David Thissen clarified a number of points in an earlier draft.     

An integrative review of process dissociation and related models in social cognition

This chapter reviews the use of formal dual process models in social psychology, with a focus on the process dissociation model and related multinomial models. The utility of the models is illustrated using studies of social and affective influences on memory, judgement and decision making, and social attitudes and stereotypes. We then compare and contrast the process dissociation model with other approaches, including implicit and explicit tests, signal detection theory, and multinomial models. Finally we show how several recently proposed multinomial models can be integrated into a single family of models, of which process dissociation is a specific instance. We describe how these process models can be used as both theoretical and measurement tools to answer questions about the role of automatic and controlled processes in social behaviour.