ISSUE: Model shows good fit, but lack statistical significance

COEFFICIENT OF DETERMINATION: One useful tool for verifying the fit of the data and the model is the coefficient of determination or R square. The value of r square tells us the percentage that the model explain the data. If the value of the coefficient of determination is low, it means that the model does not explain the data well, and vice versa. Assume that R square is high, but the test statistic shows that there is no statistical significance for the specified confidence interval---what could have been the problem?

MISSING VARIABLE: The problem of lacking statistical significance may be due to missing correct variable. The variable used is one of many---but not main one--variables that explains Y. For example, CONSUMPTION: what explain consumption? "Money"--true, but how does one explain people with money but do not consume, and people without money, but still consume? There must be more variables other than money explaining consumption. Here, the R square value would be high, but statistical test may show insignificant.

MODEL SELECTION: We need to go back to procedures for model selection. With a defined research issue, i.e. Y = dependent variable, we need to look for the correct X (independent variable) that would explain the occurrence of Y---and shows statistical significance. The problem above may come from two sources: (i) inadequate literature review; and (ii) missing variables. These two problems generally go hand-in-hand. To address the issue of inadequate literature review is to gather additional and "current" literature. The literature that we have reviewed may have been dated and change of social conditions may alter respondent's opinion, thus, giving results that do not agree with the old literature. The second problem may be addressed by regression Y and X individually and test for statistical significance. Eliminate the variable if there is no statistical significance. Go back to literature review and re-construct a new set of independent variable.

REFERENCE: See attached for SEM materials.

Rimantas wrote: "all significance tests are a function of sample size".

You have not written how big was your sample but this may be the problem.

Look at the level of the relationships between latent variables if they are high for example 0.7 and the relationship is insignificant - then the problem might be in a sample size.

If the sample is big enough and the relationships are small and insignificant may be you should revise your theory.

And finally once I experienced similar thing. I had big research sample and the relation between latent variables was big (0.8) but it was insignificant. I copied the database to another file. Sometimes program also makes mistakes. I use two programs and compare results.

With regards

Agnieszka