Irt and Lc-Irt Models for Items With Ordinal Polytomous Responses

Abstract

Item response theory (IRT) is a model-based theory in which the responses to test items depend on some person and item characteristics, according to specific probabilistic relations. The simplest and most popular are dichotomous IRT models that specify a single (i.e. unidimensional) latent trait under the assumption of normal distribution. This article reviews the latent class ordinal polytomous item response models (LC-IRT) and presents the comparison with the well-known traditional IRT models (based on the assumption of a normally distributed latent trait). The main goal of the article is to compare the estimation results of different kinds of ordinal polytomous IRT models with continuous and discrete latent variable in measuring job satisfaction in Poland. We analyzed data collected as part of the International Social Survey Programme using the ltm and MultiLCIRT packages of R.

LC and LC-IRT Models in the Identification of Polish Households with Similar Perception of Financial Position

“…[88]), model with local logit link function and both parameters being constrained. RS-GRM model (with free α j and constrained ϑ jx , global logit link function) is the rating scale version of the GRM introduced by [89], RS-GPCM (with free α j and constrained ϑ jx , local logit link function) are the rating scale versions of GPCM [90]; 1P-GRM and 1P-RS-GRM [91] are the equally discriminating versions of GRM and RS-GRM, respectively (see also [38,92] for more details).…”

LC-IRT models with covariates in Polish job satisfaction analysis

“…The RS-GRM model (with free j α and constrained jx ϑ , global logit link function) is the rating scale version of the GRM introduced by Muraki (1990), RS-GPCM (with free j α and constrained jx ϑ , local logit link function) are the rating scale versions of GPCM (Muraki, 1997); 1P-GRM 6 and 1P-RS-GRM 7 (Van der Ark, 2001) are the equally discriminating versions of GRM and RS-GRM, respectively (see Bartolucci et. al., 2016b, p. 127;Genge, 2016;Genge, 2017 for more details).…”