# Structural Equation Models I – Introduction

Instructors: Ulf H. Olsson and Njål Foldnes

## COURSE TITLE

Structural Equation Modeling 1 (SEM 1)

## PREREQUIREMENTS

Basic statistics and a course in regression (e.g. Regression I)

## COURSE CONTENT

Topics that will be covered are: Introduction to matrix notation (only some basics) and simple covariance algebra. Path diagrams and path models. Measurement models. Reliability. Exploratory and confirmatory factor analysis. Structural equation models for continuous and categorical-ordered data. Robustness issues. Some special models as the MIMIC model, the 2.order factor models, the MTMM models and multiple group models.

After undertaking this course the candidates should be able to apply and understand some classical and modern methods in multivariate statistics, use modern statistical software (R and Lisrel) and apply these on research projects. The candidates should also have acquired enough knowledge in the field to extend their statistical “tool box” on their own.

**Structure:**

- Morning session: Lectures
- Afternoon session: Exercises and software training

## LITERATURE

Book in multivariate analysis;

Ch. 2, 7, 8, 10, 11 and 15 in Jøreskog K.G; Olsson U.H & Walentin F.Y (2016) Multivariate Analysis with LISREL, Springer Series in Statistics

Rex Kline: Principles and Practice of Structural Equation Modeling, Fourth edition (2015)

## EXAMINATION PART

Term paper (100%), handed in three weeks after the course.

Supplementary aids

Lecture notes

## EXAMINATION CONTENT

See example of a term paper assignment:

Example of term paper “Problems”:

References: MVA referrers to Jöreskog, K.G., Olsson U.H., & Walentin F.Y. (2016). Multivariate Analysis with LISREL (Handout)

Figure 1: Drinking and Driving (Hint: §8.9 MVA); Structural Model

Assignment 1: CFA and SEM. Suggested software: LISREL, Mplus, R

(dataset: Drinknon.lsf; Drinknon.sav; Drinknon.dat)

a) Estimate and evaluate the CFA model (Use ML). Present measures for fit, and check if the model fits the data. Does non-normality matter, please explain how it can affect the fit of the model and other model parameters.

b) Estimate and evaluate the LISREL model depicted in figure 1. Use both ML and Robust ML. Give an interpretation of the results. Calculate the scaling factor. Are we in an Asymptotic Robust situation?

Assignment 2: Confirmatory Factor Analysis and Ordinal variables. Suggested software: LISREL, Mplus, R (Hint: § 1.6, 7.3 and 7.4 in MVA)

1.1.1.1 Political Efficacy

Coding of the variables: 1 = Strongly agree, 2 = Agree, 3 = Disagree, 4 = Disagree strongly, ((8 = Don’t know and 9 = No answer.))

a) Continuous variables

Use the data set in the file Efficacy2005.lsf (or Efficacy2005.dat; Efficacy2005.sav)

Campel et al. (1954): Political Efficacy is the feeling that individual political action does have, or can have, an impact upon political process.

Observed (measured) variables:

NOSAY: People like me have “no say” in what the government does

VOTING: Voting is the only way that people like me can have “any say” about how the government runs things.

COMPLEX: Sometimes politics and government seem so complicated that a person like me cannot really understand what is going on

NOCARE: I don’t think that public officials care much about what people like me think

TOUCH: Generally speaking, those we elect to Parliament lose touch with people pretty quickly

INTEREST: Parties are only interested in people’s votes but not in their opinions.

Test a common factor structure for the observed variables, where it is assumed that NOSAY, VOTING, COMPLEX and NOCARE load on factor 1 and TOUCH and INTEREST load on factor 2. Does non-normality matter?

b) Ordinal variables.

Use the data set in the file Efficacy2005ord.lsf (Efficacy2005ord.dat, Efficacy2005ord.sav) and test the same model as in assignment a).

Comment on your findings.