Analysis of ordinal categorical data with misclassification

We develop a method for the analysis of multivariate ordinal categorical data with misclassification based on the latent normal variable approach. Misclassification arises if a subject has been classified into a category that does not truly reflect its actual state, and can occur with one or more variables. A basic framework is developed to enable the analysis of two types of data. The first corresponds to a single sample that is obtained from a fallible design that may lead to misclassified data. The other corresponds to data that is obtained by double sampling. Double sampling data consists of two parts: a sample that is obtained by classifying subjects using the fallible design only and a sample that is obtained by classifying subjects using both fallible and true designs, which is assumed to have no misclassification. A unified expectation–maximization approach is developed to find the maximum likelihood estimate of model parameters. Simulation studies and examples that are based on real data are used to demonstrate the applicability and practicability of the proposed methods.     

Antecedents and outcomes of intervention program participation and task priority change among school psychology counselors: A latent variable growth framework

A three-year national intervention program introduced into the School Psychology Service (SPS) in Norway with the aim of increasing systemic level work among SP counselors was investigated. Latent variable growth models based on longitudinal data from 195 SP counselors gave no significant mean level change in systemic level work. This concurred with GLM analyses based on data from a sample of 20 schools. However, retrospective self-reported significant positive mean level change for systemic level work was detected among the SP counselors. Intervention program participation was associated with individual change in systemic level work. Self-efficacy beliefs about systemic level work, and school-related etiology beliefs predicted individual change to a certain degree. Comparison of two rival models gave no support for a hypothesized interaction among intervention program participation and beliefs in their effects on systemic level work. Open-ended questions indicated that individual level workload and the perceived expectations from the schools may have concern for a successful effect of the intervention program in addition to the hypothesized ones. Individual change in systemic level work was positively associated with individual change in job satisfaction.     

Estimating social and nonsocial utility functions from ordinal data

This paper reports an experiment testing two hypotheses. The first is that the value or utility associated with a payment to one's self and a payment to a co-worker can be represented as an additive function of a utility for own payment (nonsocial utility) and a utility for the difference between own and other's payment (social utility). The second hypothesis is that changes in the amount of work accomplished by one's self and/or the other should influence the social, but not the the nonsocial utilities. Support for both hypotheses is reported.     

Self-esteem and Rogers' core conditions in close friends: A latent variable pathanalysis of panel data

A LISREL or path analysis with latent variables was used to test the Rogerian-derived hypothesis that self-esteem is determined by the degree to which a person has a current close friend who is seen to be unconditionally accepting, empathic, and congruent. The revised Barrett-Lennard (1964) Relationship Inventory and Rosenberg (1965) Self-Esteem Scale were completed by 38 female and 28 male students on two occasions 15 weeks apart. The hypothesis was conjimzed for unconditionality of acceptance (which was positive) and the core conditions combined. In addition, the temporal relationships between the core conditions were analysed. Level of acceptance was reciprocally related to both empathy and congruence, while prior congruence had a negative but nonsignajicant association with unconditionality of acceptance.     

Methods for describing ordinal data with cardinal models

Several methods, both new and old, for describing ordinal data with a cardinal model are discussed in a newly developed and general context which broadens their applicability beyond their traditional use in multidimensional scaling. The relationships between the methods is investigated. It is shown that the two most commonly used methods (Guttman's rank-image principle and Kruskal's least-square monotonic transformation) are the boundary conditions of a newly proposed single parameter family of methods. An additional method is proposed which is shown to yield an equal-density model space. The commonly made distinction between “transformation” methods and “transformation-free” methods is shown to be a pseudodistinction. It is observed that all the methods can be stated as matrix operations on the model space with the conclusion that they try to optimize a linear combination of the model space.     

A general class of latent variable models for ordinal manifest variables with covariate effects on the manifest and latent variables

Previous work on a general class of multidimensional latent variable models for analysing ordinal manifest variables is extended here to allow for direct covariate effects on the manifest ordinal variables and covariate effects on the latent variables. A full maximum likelihood estimation method is used to estimate all the model parameters simultaneously. Goodness‐of‐fit statistics and standard errors are discussed. Two examples from the 1996 British Social Attitudes Survey are used to illustrate the methodology.     

Inferring latent class lexicographic rules from choice data

A lexicographic rule orders multi-attribute alternatives in the same way as a dictionary orders words. Although no utility function can represent lexicographic preference over continuous, real-valued attributes, a constrained linear model suffices for representing such preferences over discrete attributes. We present an algorithm for inferring lexicographic structures from choice data. The primary difficulty in using such data is that it is seldom possible to obtain sufficient information to estimate individual-level preference functions. Instead, one needs to pool the data across latent clusters of individuals. We propose a method that identifies latent clusters of subjects, and estimates a lexicographic rule for each cluster. We describe an application of the method using data collected by a manufacturer of television sets. We compare the predictions of the model with those obtained from a finite-mixture, multinomial-logit model.     

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).     

Psychometric network models from time-series and panel data

Researchers in the field of network psychometrics often focus on the estimation of Gaussian graphical models (GGMs)—an undirected network model of partial correlations—between observed variables of cross-sectional data or single-subject time-series data. This assumes that all variables are measured without measurement error, which may be implausible. In addition, cross-sectional data cannot distinguish between within-subject and between-subject effects. This paper provides a general framework that extends GGM modeling with latent variables, including relationships over time. These relationships can be estimated from time-series data or panel data featuring at least three waves of measurement. The model takes the form of a graphical vector-autoregression model between latent variables and is termed the ts-lvgvar when estimated from time-series data and the panel-lvgvar when estimated from panel data. These methods have been implemented in the software package psychonetrics, which is exemplified in two empirical examples, one using time-series data and one using panel data, and evaluated in two large-scale simulation studies. The paper concludes with a discussion on ergodicity and generalizability. Although within-subject effects may in principle be separated from between-subject effects, the interpretation of these results rests on the intensity and the time interval of measurement and on the plausibility of the assumption of stationarity.

     

Spousal similarity in depression: a dyadic latent panel analysis of the panel study of Belgian households

Dyadic latent panel analysis (DLPA) was applied to eight waves of the Panel Study of Belgium Households (N = 954 couples). DLPA decomposes the observed variance of both members of a dyad into variance due to stable factors, factors that gradually change over time, and occasion-specific factors including random error. Total observed similarity between members of a dyad on one occasion is decomposed into stable similarity, similarity in factors that change over time, and occasion-specific similarity. The results show that depressive symptoms are influenced by stable and changing factors and that spousal similarity in both factors contribute to spousal similarity in depression on a single occasion. Spousal similarity in factors that change gradually over time suggests that shared-environmental factors contribute to depressive symptoms.     

Measuring patterns of change in personality assessments: an annotated application of latent growth curve modeling

Latent growth curve (LGC) modeling within the framework of structural equation modeling (SEM) is now highly regarded as one of the most powerful and informative approaches to the analysis of longitudinal data (see, e.g., Curran & Hussong, 2003). Whereas LGC modeling enables researchers to test for differences in developmental trajectories across time, conventional repeated measures analyses do not provide this opportunity. Nonetheless, a review of studies reported in most psychology journals reveals scant application of this methodological approach. One possible explanation for this limited use of LGC modeling is a lack of knowledge related to its application. The intent of this article, then, is to address this deficiency by presenting an annotated application of LGC modeling to health psychology data. Based on a sample of 405 Hong Kong Chinese women who recently underwent breast cancer surgery, we walk the readers through SEM modeling procedures that test for differences in both the initial status and rate of change in Psychological Morbidity and Social Adjustment at 1, 4, and 8 months postsurgery. We interpret findings from both a methodological and a substantive perspective.     

Infants and I scales: Inferring change from the ordinal stimulus selections of infants for configural stimuli

The analysis of I-scale preference orders of 71 infants 2 to 9 months old to four face-like stimuli suggested a common J-scale stimulus ordering for each of the four age groups. Changes in I-scale frequencies were used as a measure of age-related changes in preference orders. Results revealed no change in preference for the age period studied. Together with other data these results suggest an ageinvariant preference for organized face-like forms from at least as early as five weeks through 9 months. This finding is at variance with some theoretical expectations. A Thurstone analysis is provided as a contrast to the J-scale analysis. Assumptions of different data analyses are considered as the basis for varying results reported in the literature.     

On the power of multivariate latent growth curve models to detect correlated change

We evaluated the statistical power of single-indicator latent growth curve models (LGCMs) to detect correlated change between two variables (covariance of slopes) as a function of sample size, number of longitudinal measurement occasions, and reliability (measurement error variance). Power approximations following the method of Satorra and Saris (1985) were used to evaluate the power to detect slope covariances. Even with large samples (N = 500) and several longitudinal occasions (4 or 5), statistical power to detect covariance of slopes was moderate to low unless growth curve reliability at study onset was above .90. Studies using LGCMs may fail to detect slope correlations because of low power rather than a lack of relationship of change between variables. The present findings allow researchers to make more informed design decisions when planning a longitudinal study and aid in interpreting LGCM results regarding correlated interindividual differences in rates of development.     

The role of change in the relationship between commitment and turnover: a latent growth modeling approach

Through the use of affective, normative, and continuance commitment in a multivariate 2nd-order factor latent growth modeling approach, the authors observed linear negative trajectories that characterized the changes in individuals across time in both affective and normative commitment. In turn, an individual's intention to quit the organization was characterized by a positive trajectory. A significant association was also found between the change trajectories such that the steeper the decline in an individual's affective and normative commitments across time, the greater the rate of increase in that individual's intention to quit, and, further, the greater the likelihood that the person actually left the organization over the next 9 months. Findings regarding continuance commitment and its components were mixed.     

Ridge structural equation modelling with correlation matrices for ordinal and continuous data

This paper develops a ridge procedure for structural equation modelling (SEM) with ordinal and continuous data by modelling the polychoric/polyserial/product‐moment correlation matrix R . Rather than directly fitting R , the procedure fits a structural model to R _a= R +a I by minimizing the normal distribution‐based discrepancy function, where a > 0. Statistical properties of the parameter estimates are obtained. Four statistics for overall model evaluation are proposed. Empirical results indicate that the ridge procedure for SEM with ordinal data has better convergence rate, smaller bias, smaller mean square error, and better overall model evaluation than the widely used maximum likelihood procedure.     

Dynamic analysis of multivariate panel data with non-linear transformations

Many models for multivariate data analysis can be seen as special cases of the linear dynamic or state space model. Contrary to the classical approach to linear dynamic systems analysis, in which high-dimensional exact solutions are sought, the model presented here is developed from a social science framework where low-dimensional approximate solutions are preferred. Borrowing concepts from the theory on mixture distributions, the linear dynamic model can be viewed as a multi-layered regression model, in which the output variables are imprecise manifestations of an unobserved continuous process. An additional layer of mixing makes it possible to incorporate non-normal as well as ordinal variables.Using the EM-algorithm, we find estimates of the unknown model parameters, simultaneously providing stability estimates. The model is very general and cannot be well estimated by other estimation methods. We illustrate the applicability of the obtained procedure through an example with generated data.