Vol. III (LXV) No. 2/2013 78 - 88 Applying confirmatory factor analysis to evaluate the fit of measurement models in education and psychological assessment Wahyu Widhiarso a , Ji í Kožený b, * a Gadjah Mada University, Jl. Humaniora No 1, Yogyakarta 55281, Indonesia b Prague Psychiatric Center, Ustavni 91, Prague 8 – Bohnice, 181 03 , Czech Republic Abstract Confirmatory factor analysis (CFA) was used to verify three measurement models as defined by classical test theory for three scales that represent a wide range of individual attributes and are manifested in various indicators. The congeneric measurement model represents a general true score model whereas the others represent restrictions on congeneric model it. It is assumed that congeneric model will match the characteristics of all of these measures. Accordingly, we hypothesized that the congeneric model will fit to the data. Analysis results suggest that the congeneric measurement model appears to be the best fit for the data. Based on our findings, we recommend that it is important to make a distinction of which measurement model fits to the data before continuing into further analysis. Keywords: statistics; model; measurement; congeneric; personality 1. Introduction Every statistical method is developed under particular assumptions. However, when employing one of those methods, most researchers are not concerned with whether the assumptions of the underlying method were satisfied or not. For example, most researchers arbitrarily use coefficient alpha for estimating reliability of measurement. Socan (2000) and Graham (2006) found that a lot of researchers merely focus on using Cronbach's alpha coefficient but they are unaware of the several underlying assumptions of this. If the data sets do not satisfy the assumption, then the alpha coefficient will underestimate the true reliability of the measure. Psychometricians have warned that underlying assumptions should be satisfied in order to provide the accurate information about the measure. Both classical test (CTT) and modern theory (IRT) have a certain viewpoint on evaluating measurement, namely the measurement model. The measurement model describes the relationship among measurement elements. For example, the CTT measurement model defines the relationship between the trait being measured and its indicators. In IRT, it defines the relationship between the level of trait and the probability of getting a certain score. The measurement model is built based on certain assumptions about the relationship between the indicator and the attribute to be measured. Furthermore, all psychometric methods are rooted in a measurement model. In other words, the measurement model has become the basis of the emergence of various methods to evaluate the psychometric properties of the measure. 1.1. Measurement Model The word “model” as a part of the phrase “measurement model” is often used interchangeably with “theory”, “test”, “item” or “form”. However, they have a similar meaning since they define the link between measurable indicators and latent * Corresponding author. Tel.: +62 274550435; fax. +62 274550436 E-mail address: wahyu_psy@ugm.ac.id