A multidimensional item response model: Constrained latent class analysis using the gibbs sampler and posterior predictive checks

Hoijtink, Herbert; Molenaar, Ivo W.

doi:10.1007/bf02295273

Cited by 88 publications

(73 citation statements)

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“…In this section, the data with respect to antisocial behaviour will be analyzed using confirmatory latent class analysis (CLCA) (Hoijtink, 1998(Hoijtink, , 2001Hoijtink & Molenaar, 1997). This approach consists of four steps.…”

Section: The Dimensions Of Antisocial Behaviourmentioning

confidence: 99%

“…The total set of the predictions will be called model TSP 12344*. Hoijtink and Molenaar (1997) present the latent class equivalent of a nonparametric item response model that might be appropriate for the data at hand. The five-class version of this model is presented in Table 8.…”

Section: The Theorymentioning

confidence: 99%

“…In Table 3, estimates of the parameters can be found of the three-class exploratory model. These estimates are obtained using Bayesian computational statistics; the interested reader is referred to Hoijtink and Molenaar (1997) and Hoijtink (1998). Each class gets a weight, that is the proportion of persons belonging to that class, and each class has its own class-specific probabilities, that is the probability of answering ''yes'' to each of the items.…”

mentioning

confidence: 99%

“…The plausibility of real scientific progress is larger if the current state of affairs (existing knowledge and theories) is properly accounted for in the statistical models used for the analysis. In this paper a specific form of confirmatory latent class analysis (CLCA) will be proposed (Hoijtink, 1998(Hoijtink, , 2001Hoijtink & Molenaar, 1997). It will be shown how theories can be translated into a CLCA using inequality constraints among the parameters of the model.…”

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confidence: 99%

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Applications of confirmatory latent class analysis in developmental psychology

Laudy

Zoccolillo

Baillargeon

et al. 2005

European Journal of Developmental Psychology

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In the field of developmental, psychology researchers may have several competing theories with respect to their research subject. In this paper an approach will be proposed that can be used to select the best of these theories. It will be shown that a theory can be translated in a constrained latent class model using inequality constraints. This can be done for several (possibly competing) theories. Subsequently, fit-measures can be used to determine which model (and thus which theory) is supported most by the data. The approach will be introduced using data with respect to self-reported child and adult antisocial behaviour. It will be further illustrated using data obtained using the figural intersection task.Exploratory latent class analysis (ELCA) (Clogg, 1981;Goodman, 1974;Haberman, 1988;Vermunt, 1996) latent classes. In developmental psychology, for example, data with respect to some cognitive ability of children, like responses to items on Piaget's balance scale task, Piaget's water level task or the figural intersection task can be subjected to an ELCA. This can result in groups of children using different strategies (e.g., Boom, Hoijtink, & Kunnen, 2001;Jansen & van der Maas, 1997;Pascual-Leone & Baillargeon, 1994) and the transitions between the groups (Hoben & Hettmansperger, 2001). For a methodological overview and applications see von Eye and Clogg (1994).A key question in ELCA is: into how many homogeneous subgroups should the sample be divided? Usually fit measures (Everitt, 1988;Lin & Dayton, 1997) are used to determine which number of classes is optimal. Furthermore, the resulting classes have to be interpreted. To illustrate this, consider an ELCA of the responses of 2001 women to several items with respect to self-reported child and adult antisocial behaviours. In order to assess maternal antisocial disorder, the mothers were asked about five childhood antisocial behaviours and four adult behaviours. In Table 1 the items (responses to either ''yes'' or ''no'' questions) and the response percentages can be found. The women were mothers of 5-month-old infants 2 LAUDY ET AL.from a population-based longitudinal study of the development of children of the province of Quebec, Canada (Jette, Desrosiers, Tremblay & Thibault, 2000;Zoccolillo, 2000).In the top panel of Table 2, three fit measures for exploratory analyses with two, three, and four classes are displayed. Hoijtink (1998Hoijtink ( , 2001 developed these fit measures to be able to select the best of a number of exploratory and confirmatory (see below) latent class models. The first measure is 72 log of the marginal likelihood (Kass & Raftery, 1995). This measure can be seen as the Bayesian counterpart to information criteria like AIC, CAIC and BIC (Kass & Raftery, 1995). It is a relative (with respect to the corresponding numbers for other models) fit measure: the smaller the number the better the model. If, a priori, each model is considered to be equally good, 72 log of the marginal likelihood can be transformed to posterior probabilities ...

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Section: The Dimensions Of Antisocial Behaviourmentioning

confidence: 99%

Section: The Theorymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Applications of confirmatory latent class analysis in developmental psychology

Laudy

Zoccolillo

Baillargeon

et al. 2005

European Journal of Developmental Psychology

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“…It was especially the Gibbs sampler (Geman & Geman, 1984) that received much attention, since it facilitates sampling from complex multivariate posterior distributions, and as such, solves estimation problems for models which lead to great difficulty in a (marginal) maximum likelihood framework (Bock & Lieberman, 1970;Bock & Aitken, 1981). The MCMC revolution has also found its way into psychometrics, where it has been popularized by Albert (1992) and Patz and Junker (1999b), with further applications to the estimation of models for testlets (Bradlow, Wainer, & Wang, 1999), latent classes (Hoijtink & Molenaar, 1997), multilevel IRT models (Fox & Glas, 2001), random item parameters (Janssen, Tuerlinckx, Meulders, & de Boeck, 2000), and multidimensional IRT models (Béguin & Glas, 2001).…”

Section: Introductionmentioning

confidence: 99%

Plausible values in statistical inference

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Latent Class and Latent Transition Analysis

Lanza

Flaherty

Collins

2003

Handbook of Psychology

323

281

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A multidimensional item response model: Constrained latent class analysis using the gibbs sampler and posterior predictive checks

Abstract: Gibbs sampler, posterior predictive checks, nonparametric item response theory, multidimensional, manifest monotonicity, local homogeneity, conditional association,

Cited by 88 publications

References 40 publications

Applications of confirmatory latent class analysis in developmental psychology

Applications of confirmatory latent class analysis in developmental psychology

Plausible values in statistical inference

Latent Class and Latent Transition Analysis

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