Measurement Invariance with Ordered Categorical Variables

Multi-item ordered categorical scales and structural equation modelling approaches are often used in panel research for the analysis of latent variables over time. The accuracy of such models depends on the assumption of longitudinal measurement invariance (LMI), which states that repeatedly measured latent variables should effectively represent the same construct in the same metric at each time point. Previous research has widely contributed to the LMI literature for continuous variables, but these findings might not be generalized to ordered categorical data. Treating ordered categorical data as continuous contradicts the assumption of multivariate normality and could potentially produce inaccuracies and distortions in both invariance testing results and structural parameter estimates. However, there is still little research that examines and compares criteria for establishing LMI with ordinal categorical data. Drawing on this lack of evidence, the present chapter offers a detailed description of the main procedures used to test for LMI with ordered categorical variables, accompanied by examples of their practical application in a two-wave longitudinal survey administered to 1,912 Italian middle school teachers. The empirical study evaluates whether different testing procedures, when applied to ordered categorical data, lead to similar conclusions about model fit, invariance, and structural parameters over time.

Assessment of Climate Change in Italy by Variants of Ordered Correspondence Analysis

This paper explores climate changes in Italy over the last 30 years. The data come from the European observation gridded dataset and are concerned with the temperature throughout the country. We focus our attention on two Italian regions (Lombardy in northern Italy and Campania in southern Italy) and on two particular years roughly thirty years apart (1986 and 2015). Our primary aim is to assess the most important changes in temperature in Italy using some variants of correspondence analysis for ordered categorical variables. Such variants are based on a decomposition method using orthogonal polynomials instead of singular vectors and allow one to easily classify the meteorological station observations. A simulation study, based on bootstrap sampling, is undertaken to demonstrate the reliability of the results.

The goalkeeper influence on ball possession effectiveness in futsal

The aim of this study was to identify which variables were the best predictors of success in futsal ball possession when controlling for space and task related indicators, situational variables and the participation of the goalkeeper as a regular field player or not (5 vs. 4 or 4 vs. 4). The sample consisted of 326 situations of ball possession corresponding to 31 matches played by a team from the Spanish Futsal League during the 2010–2011, 2011–2012 and 2012–2013 seasons. Multidimensional qualitative data obtained from 10 ordered categorical variables were used. Data were analysed using chi-square analysis and multiple logistic regression analysis. Overall, the highest ball possession effectiveness was achieved when the goalkeeper participated as a regular field player (p<0.01), the duration of the ball possession was less than 10 s (p<0.01), the ball possession ended in the penalty area (p<0.01) and the defensive pressure was low (p<0.01). The information obtained on the relative effectiveness of offensive playing tactics can be used to improve team’s goal-scoring and goal preventing abilities.