Teoria reakcji na pozycję w podejściu modelowym w taksonomii / Item response theory in model-based clustering

Abstract

JEL Classification: C55Streszczenie: Teoria reakcji na pozycję (item response theory) zaliczana jest do jednego z dwóch nurtów metodologicznych w ocenie rzetelności skali. Z kolei analizę klas ukrytych (latent class analysis) można wpisać w nurt podejścia modelowego w taksonomii, wykorzystującego ideę mieszanek rozkładów. Modele te wykorzystywane są do analizy jakościowych zbiorów danych o niejednorodnej strukturze, w których liczba klas jest nieznana (tzw. zmienna ukryta). W ostatnim czasie na popularności zyskuje podejście modelowe w taksonomii, łączące teorię reakcji na pozycje z modelami klas ukrytych. Celem pracy jest przedstawienie propozycji wykorzystania podejścia modelowego w taksonomii, wykorzystującego teorię IRT w analizie zdolności do oszczędzania w polskim społeczeństwie. Badania przeprowadzone będą z zastosowaniem pakietu MultiLCIRT programu R.Słowa kluczowe: teoria IRT, analiza klas ukrytych, podejście modelowe w taksonomii. Summary: Item response theory is considered to be one of the two trends in methodological assessment of the reliability scale. In turn, latent class models can be viewed as a special case of model-based clustering, for heterogenous multivariate discrete data. We used the approach combining item response theory and latent class models to find groups of Polish households' with similar saving ability levels. We analyzed data collected as part of the Polish Social Diagnosis using MultiLCIRT package of R.

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

“…It's worth noting that, the class of LC-IRT models is more flexible because compared to traditional IRT models is not based on the restrictive assumption such as normality of the latent trait (is based on discreteness assumption) and at the same time allows also for multidimensional structure of it (see [39,100]). Those assumption may be especially useful in real data analyzes, described by many response variables where the normality and unidimensional assumptions of the latent trait (explicitly introduced) are very often restrictive to fulfill.…”

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

“…However it is worth noting that this extension of the traditional IRT (i.e. LC-IRT) models, by introducing assumptions of discreteness and also multidimensionality of latent trait (see [Bartolucci et al 2014;Genge 2016]) may be especially useful in socio-economic data analyses where the normality and unidimensional assumptions of the latent trait (explicitly introduced) are very often restrictive to fulfill.…”

“…As far as the discrete approach is concerned (analysis under discrete distribution for the ability), we followed the consecutive ordered steps [Bacci et al 2014;Bartolucci et al 2014;Genge 2016]. The optimal number of clusters was chosen using information criteria for the basic model.…”

“…1 Because the context of the empirical study (the comparison with IRT models under continuous approach of the (unidimensional) latent trait) and because the polytomous items considered in the empirical part of the study cannot be a priori divided between more than one dimension we will consider the unidimensional latent trait for the LC approach as well compare [Bacci et al 2014;Bartolucci et al 2016b;Genge 2016]).…”

A Comparison of Dichotomous Irt Models Based on Continuous and Discrete Latent Trait – Polish Households’ Saving Skills

“…Then, a crucial point in applying the discrete approach was the choice of the number of support points of the latent trait. The number of the latent classes (support points) was set to s = 3, in accordance with the previous studies carried out with the same data (see for details [Genge 2016]). Finally, both approaches based on continuous and discrete latent distribution of the latent trait were compared (based on AIC and BIC criteria, see Table 1).…”