These guidelines are merely rules of thumb, however, and now questioned by many authorities.Its origins can be traced back to Psychologist Charles Spearman at the turn of the 20th century and Geneticist Sewall Wright in the immediate aftermath of WWI.Many others have had a hand in its development, notably Karl Jreskog and Peter Bentler.
![]() We can only make inferences about them from what we can observe, responses to questionnaire items, for example. Measuring latent constructs is challenging and we must also incorporate estimates of measurement error into our models. Also, when multicollinearity - highly correlated independent variables - is a concern, SEM is the tool of choice for many researchers. Sometimes, however, variables are combined (parceled) on empirical or theoretical grounds prior to analysis and the measurement model plays no role. At other times we are not concerned with measurement error and only the raw variables - observed variables in SEM jargon - are used. When there is no measurement model - only the structural model - the term Path Analysis is more appropriate than SEM, though some use SEM very generally. In its modern forms it is able to be used with any data type - ratio, interval, ordinal, nominal and count - and can model curvilinear relationships among variables as well as interactions. It can accommodate multiple dependent variables and is sometimes blended with Conjoint Analysis. SEM can also be used to adjust for individual response styles in consumer surveys and other questionnaire data. For the technically-inclined among you, SEM can be estimated with Maximum Likelihood or Bayesian approaches. Though not a simple modeling task, SEM would be appropriate for these objectives, and the images of brands could also be mapped to help us understand how the dimensions underlying brand perceptions distinguish the brands. This illustration is a simplified and cloaked version of the full model, which included many more attributes as well as exogenous variables such as age. ![]() These are theoretical concepts which can be inferred but not directly measured. In this example, the Traditional factor is represented by, or measured by, the attributes Prestigious, Big Brand and Reliable. The single-headed arrows running from the latent variables to the attributes are equivalent to loadings in Factor Analysis. In SEM, regression coefficients are normally smaller than correlations and loadings, as they are here. This is not always the case and there are times when entirely different models are necessary. Mixture Modeling is very tricky but worth the effort when done competently. Sometimes we conclude that one overall model is sufficient - negative findings are also important.
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