For instance my model has five constructs, why should I report three or four factor model ? Also what is common factor model and how is this used to test CMV ?
Sometimes, people test competing theories about the factor structure underlying a set of observed (measured) variables (e.g., items, scales). One theory may predict 3 factors, another theory 4 factors etc. That's why people sometimes test multiple models with different numbers of factors. You don't have to do this if your only goal is to test the hypothesized five-factor structure. In that case, you may choose to only estimate a single CFA model with the 5 factors that you predict.
"Common factor model" refers to the fact that in many CFA models, multiple indicators (e.g., items, scales) are hypothesized to measure the same (i.e., their "common") factor or latent variable.
So to test common factor model, I need to connect items of all five factors (in my case) to one latent factor, and check what or how do I interprete the results ?
Hello Abdul,
First, decide whether you are trying to confirm/disconfirm some specific model (confirmatory factor analysis) or trying to use exploratory factor analysis to help identify a plausible model for your set of observed variables.
If CFA, decide what model you believe (based on theory, prior research, related studies using same/similar observed and latent variables) _should_ be operative. Then set that model up in AMOS (or any SEM software you might choose to use, there are many) and evaluate it. As Christian Geiser notes, it is not uncommon for analysts to set up competing models and evaluate those as well as a target model. That way, one can make statements as to how well (or poorly) the target model fares compared to competing models.
IF EFA, then you'll need to make a host of decisions, starting with what method of factor extraction to use (for example: maximum likelihood, principal axis, or other), what rule to use for determining number of factors (parallel analysis, scree test, eigenvalue > 1 criterion, or something else), what method of rotation to use if more than one factor is extracted, and what salience criterion to apply to declare a variable as affilitated with a factor. From these, one can usually (but not always!) identify at least one plausible model. As this process is often iterative, it makes sense to then use CFA to determine how well that model works with a new/different data set.
There's nothing about the common factor model that requires a single factor solution. It's just that you're asserting that a number of manifest/observed/indicator variables have one or more common underpinnings (the common factor/s).
Good luck with your work.