The aim of this study is to investigate the presence of DIF over the gender variable with the latent class modeling approach. Data were 880 students from the USA who participated in the PISA 2018 8th-grade financial literacy assessment. Latent class analysis (LCA) approach was used to determine the latent classes and the data fit the three-class model better in line with fit indices. To obtain more information about the characteristics of the emerging classes, uniform and non-uniform DIF sources were determined by using the Multiple Indicator Multiple Causes (MIMIC) model. The findings are very important in terms of contributing to the interpretation of latent classes. According to the results, the gender variable is a potential source of DIF for latent class indicators. Gathering unbiased estimates for the measurement and structural parameters, it is important to include direct effects in the classes. Ignoring these effects can lead to incorrect determination of implicit classess. An example of the application of Multiple Indicator Multiple Causes (MIMIC) model showed in a latent class framework with a stepwise approach with this study.

This study examined the existence of latent classes in TIMSS 2015 data from three countries, Singapure, Turkey and South Africa, were analyzed using Mixture Item Response Theory (MixIRT) models (Rasch, 1PL, 2PL and 3PL) on 18 multiple-choice items in the science subtest. Based on the findings, it was concluded that the data obtained from TIMSS 2015 8th grade science subtest have a heterogeneous structure consisting of two latent classes. When the item difficulty parameters in two classes were examined for Singapore, it was determined that the items were considerably easy for the students in Class 1 and the items were easy for the students in Class 2. When the item difficulty parameters in two classes were examined for Turkey, it was found that the items were easy for the students in Class 1 and the items were difficult for the students in Class 2. When the item difficulty parameters in two classes were examined for South Africa, it was ascertained that the items were a bit easy for the students in Class 1 and the items were considerably difficult for the students in Class 2. The findings were discussed in the context of the assumption of parameter invariance and test validity.

This study aims to examine the effects of mixture item response theory (IRT) models on item parameter estimation and classification accuracy under different conditions. The manipulated variables of the simulation study are set as mixture IRT models (Rasch, 2PL, 3PL); sample size (600, 1000); the number of items (10, 30); the number of latent classes (2, 3); missing data type (complete, missing at random (MAR) and missing not at random (MNAR)), and the percentage of missing data (10%, 20%). Data were generated for each of the three mixture IRT models using the code written in R program. MplusAutomation package, which provides the automation of R and Mplus program, was used to analyze the data. The mean RMSE values for item difficulty, item discrimination, and guessing parameter estimation were determined. The mean RMSE values as to the Mixture Rasch model were found to be lower than those of the Mixture 2PL and Mixture 3PL models. Percentages of classification accuracy were also computed. It was noted that the Mixture Rasch model with 30 items, 2 classes, 1000 sample size, and complete data conditions had the highest classification accuracy percentage. Additionally, a factorial ANOVA was used to evaluate each factor's main effects and interaction effects.

This study aimed to investigate the heterogeneity of the TIMSS 2015 data from Turkey and the USA 8th grade math. Latent Class Analysis (LCA) was used to determine the latent classes that cause heterogeneity in the data by using categorical observed variables. As a result of the LCA, supporting absolute and relative model fit indices through AvePP and entropy values, it was concluded that the data obtained from both countries fit the three-class model. The latent class probabilities and conditional response probabilities were examined for homogeneity and degree of segregation of the classes from each other. Based on the findings, it is recommended that the assumption of homogeneity in international evaluations be evaluated empirically with LCA. With this article, an example of the application of LCA is provided, and it is believed to be useful for researchers in the context of education and psychological evaluation.

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