Measurement Models and CFA Ulf H. Olsson Professor of Statistics

Ulf H. Olsson Factor Analysis Exploratory Factor Analysis (EFA) One wants to explore the empirical data to discover and detect characteristic features and interesting relationships without imposing any definite model on the data Confirmatory Factor Analysis (CFA) One builds a model assumed to describe, explain, or account for the empirical data in terms of relatively few parameters. The model is based on a priori information about the data structure in form of a specified theory or hypothesis

Ulf H. Olsson The EFA model

Ulf H. Olsson EFA Eigenvalue of factor j The total contribution of factor j to the total variance of the entire set of variables Comunality of variable i The common variance of a variable. The portion of a variable’s total variance that is accounted for by the common factors

Ulf H. Olsson The CFA model In a confirmatory factor analysis, the investigator has such a knowledge about the factorial nature of the variables that he/she is able to specify that each xi depends only on a few of the factors. If xi does not depend on faktor j, the factor loading lambdaij is zero

Ulf H. Olsson Measurement Models Consequences of Measurement Error Biased estimates Does the Model fit the Data The Chi-square test The RMSEA approach Detailed evaluation of the model Reliability Validity

Ulf H. Olsson CFA and ML k is the number of manifest variables. If the observed variables comes from a multivariate normal distribution, and the model holds in the population, then

Ulf H. Olsson Testing Exact Fit

Ulf H. Olsson Problems with the chi-square test The chi-square tends to be large in large samples if the model does not hold It is based on the assumption that the model holds in the population It is assumed that the observed variables comes from a multivariate normal distribution => The chi-square test might be to strict, since it is based on unreasonable assumptions?!

Ulf H. Olsson Alternative test- Testing Close fit

Ulf H. Olsson How to Use RMSEA Use the 90% Confidence interval for EA Use The P-value for EA RMSEA as a descriptive Measure RMSEA< 0.05 Good Fit 0.05 < RMSEA < 0.08 Acceptable Fit RMSEA > 0.10 Not Acceptable Fit

Ulf H. Olsson Other Fit Indices CN RMR GFI AGFI Evaluation of Reliability MI: Modification Indices

Ulf H. Olsson Nine Psychological Tests