Local homogeneity in latent trait models. A characterization of the homogeneous monotone irt model

Abstract

stochastic subject, unidimensionality, local independence, experimental independence, local homogeneity, monotonicity, subpopulation invariance, pairwise determination, nonnegative association,

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

“…It is attractive to use a model that is based on desirable measurement properties but does not impose the restrictions of a parametric family on the item response functions nor on the ability distribution. This paper will be based on NIRM that can be defined using the properties of monotonicity (M), conditional independence (CI), restricted or uni-dimensionality (RD/UD) (see, for example, Mokken, 1971, p. 77, p. 118; also Holland, 1981;Holland & Rosenbaum, 1986;Junker, 1993;Rosenbaum, 1984;Sijtsma & Molenaar, 1987), and marginal local homogeneity (MLH; Ellis & van den Wollenberg, 1993). Other NIRM with additional or different properties could be similarly treated.…”

Statistical Models for the Development of Psychological and Educational Tests

“…Because of their generality, nonparametric models have proven to be excellent starting points for deriving properties of IRT models in general (e.g., Ellis & Van den Wollenberg, 1993;Hemker et al, 1997;Holland & Rosenbaum, 1986;Junker, 1991Junker, , 1993Stout, 2002). For example, Ellis and Van den Wollenberg (1993) showed that IRT models in general are true for subpopulations that have the same e but not for individual respondents.…”

“…For example, Ellis and Van den Wollenberg (1993) showed that IRT models in general are true for subpopulations that have the same e but not for individual respondents. This implies th at for a particular e value, say ed, a response probability like P(Xj = lied) = 0.7 (dichotomous scoring) means that 70% of the respondents having the same ed provide a 1 score and 30% a 0 score, whereas the same individual is assumed to provide the same item score across independent replications.…”

Developments in Measurement of Persons and Items by Means of Item Response Models

“…[It may be noted, by the way, that a distinction can be made between respondents and Os and, related to this, different definitions of the response probability; see Holland (1990) and Ellis and Van den Wollenberg (1993). We will ignore this distinction here for practical purposes.]…”