Before doing comparative research with SEM …

1. Before doing comparative research with SEM … Prof. Jarosław Górniak Institute of Sociology Jagiellonian University Krakow

2. What is worth to consider • Think about your theory • Check your data • Explore your data • Build your model carefully • Think about survey error: • Systematic => Are the country samples representative? Is the non-response properly addressed? • Sampling variance => Is it computed properly? Consequently: are our model tests properly computed?

3. Example:Factors influencing attitudes towards money (selection of hypothesis) • Permanent income (long-term income potential) seems to be more predictive for saving - socio-economic status may be treated as proxy indicator of permanent income. • Economic optimism or pessimism related to: — experienced changes in income situation;— expectations of future income situation • Stage of life cycle (finding of consumer behaviour research in the field of retail banking) • Patterns of lifestyles (differences between rural and urban settlements) • Feeling of being threatened – a working hypothesis

4. Exploratory data analysis – theory driven insight into data

5. Exploratory analysis – insight into comparative data (digression)

6. Exploratory analysis – insight into comparative data (digression)

7. Exploratory analysis – insight into comparative data (digression)

8. Exploratory analysis – insight into comparative data (digression)

9. Back to the topic

10. General idea of the path model

11. Attitude towards debt – one factor solution

12. Attitude towards debt – three factors solution

13. Attitude towards debt – hierarchical CFA

14. Psychographics – problem with correlated error terms

15. Structural model – non-correlated error terms

16. Hybrid model – using parcels in SEM • Hybrid model: includes a combination of latent and observed variables • Parcels are indexes computed by summing or averaging 2 or more items • More reliable than items • More normally distributed than items • Usually higher loadings and better fit • Less problems with identification, especially compared with hierarchical factor models • The use of parcels is controversial • Is less controversial if scaling diagnostics is done: • Using parcels you better check for unidimensionality • Using parcels check in FA if the loadings of the items are similar • Determine reliability

17. Structural model – correlated error terms

18. SEM are not causal models

19. Single indicator constructs – using reliability information • Using single indicator (like SES scale): • fix the variance of indicator error term at the level =(1-alpha)*variance of the indicator • If the scale is standardised (automatically done in optimal scaling like MCA) – the formula simplifies • Fix the loading of this indicator at 1 • The reliability information can be used in terms of any indicator with known reliability

20. Structural model – using known reliability of the scale

21. Structural model – using known reliability of the scale

22. Structural model – using known reliability of parcels

23. Structural model – using reliability of parcels: model fit

24. Topics which are usually less considered in SEM context but are very important • Complex samples and SEM • Sampling variance changed by clustering, stratification and weighting for non equal inclusion probabilities • Weighting not always available (like in AMOS) • Non-response and SEM: • Item non-response – solutions exists • Special estimation algorithms (like in AMOS) • Imputation before analysis • Survey non-response • Falling response rates – what populations we model? • The non-response mechanism is not MAR (Missing Completely at Random) • Usual post-hoc solution is weighting for non-response but not always possible in SEM (AMOS) • Addressing systematic error increases sampling variance, but this is not considered in popular SEM applications

25. Before doing comparative research with SEM… • Check if your theory is plausible • Think about your model, construct definitions and indicators before fieldwork • Examine your data, also secondary data • Explore your data with theoretical background • Build your SEM model carefully • Check alternative models • Think about survey error and … do something about it!