## 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.
**Basic reading**- Hair et al., Chapter 11: SEM: Confirmatory factor analysis
- Meyers et al., Chapter 13A: Confirmatory factor analysis, Chapter 13B: Confirmatory factor analysis using AMOS.
**Advanced reading**- 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.
**Basic reading**- 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.
**Advanced reading**- 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.
**Basic reading**- Field, Chapter 16, sections 16.5-16.11.
**Advanced reading**- .
**Software****Reporting Loglinear analysis in publications****Reporting - examples in journal articles**