 ## Statistics & Methods Centre - Confirmatory analysis

Confirmatory multivariate interdependence techniques aim to confirm hypothesised relationships between variables making explicitly assumptions about the distributions of the variables. The idea is to test the hypothesised patterns and if necessary check alternative hypotheses against each other. Most methods lean heavily on the normal distributions but methods using other types of assumptions are available as well, in particular for categorical data. The loglinear models on this page are not really confirmatory.
A brief characterisation of the major textbooks referred to here can be found on the Basic statistics textbooks

Confirmatory factor analysis
Confirmatory factor analysis is a method to estimate and fit a specific, theory-driven model for the relationships between observed measurements and latent variables or factors. This model is a standard part of structural equation models.
Hair et al., Chapter 11: SEM: Confirmatory factor analysis
Meyers et al., Chapter 13A: Confirmatory factor analysis, Chapter 13B: Confirmatory factor analysis using AMOS.
McDonald, R.P. (1985). Factor analysis and related methods. Hillsdale NJ: Erlbaum.
Brown, T.A. (2006). Confirmatory factor analysis for applied research. New York: The Guilford Press.
Software
Not included in SPSS, use packages for Structural equation modeling, such as EQS, Lisrel, MPlus, and AMOS (see below)
Annotated output for EQS - Hanneman site
Byrne, B.M. (various years).Structural equation modeling with xxx. Mahwah NJ: Erlbaum. [where xxx=Lisrel, EQS, or AMOS]
Reporting Confirmatory factor analysis in publications
Reporting - examples in journal articles

Structural equation models
Structural equation modelling refers to a series of techniques to estimate and fit specific, theory-driven models for the relationships between observed measurements and latent variables or factors (the measurement model) and between latent variables (the structural model). Such models are generally visualised with path diagrams, and can be formulated in terms of sets of regression equations in which the measurement part consist of observed response variables and latent predictors, while the structural part consists of response and predictor variables which are both unobserved or latent.
Hair et al., Chapter 10: Structural equation modeling: An introduction; Chapter 11: SEM: Confirmatory factor analysis; Chapter 12: SEM: Testing a structural model.
Meyers et al., Chapter 14A: Causal modeling: Path analysis and structural equation modeling, Chapter 14B: Path analysis using SPSS and AMOS.
Raykov, T., & Marcoulides, G.A. (2006) A first course in structural equation modeling. Mahwah NJ: Erlbaum
Software
Not included in SPSS, use dedicated packages for Structural equation modeling, such as EQS, Lisrel (Free student edition), MPlus, and AMOS (see below)
Many examples are contained in the manuals of the respective computer programs.
Overview of free documentation - Lisrel site
Overview of examples - Lisrel site
Byrne, B.M. (various years).Structural equation modeling with xxx. Mahwah NJ: Erlbaum. [where xxx=Lisrel, EQS, or AMOS]
Reporting Confirmatory factor analysis in publications
Reporting - examples in journal articles

Loglinear analysis
Loglinear analysis is a technique to analyse multiway contingency tables by specifying anova-like models for the logarithms of the expected frequencies. Typical models consist of main effects and one or more interactions between the variables making up the table.