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

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?

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

Exploratory data analysis – theory driven insight into data

Exploratory analysis – insight into comparative data (digression)

High position in social stratification Low position in social stratification Politically active Conductors of Change Active Citizens Politically passive Passive Experts Silent Citizens

Exploratory analysis – insight into comparative data (digression)

Back to the topic

General idea of the path model

Attitude towards debt – one factor solution

Attitude towards debt – three factors solution

Attitude towards debt – hierarchical CFA

Psychographics – problem with correlated error terms

Structural model – non-correlated error terms

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

Structural model – correlated error terms

SEM are not causal models

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

Structural model – using known reliability of the scale

Structural model – using known reliability of parcels

Structural model – using reliability of parcels: model fit

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

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!