Hello Chlotilde,

The list of possible reasons is spot on. Unless you tried to minimize missing data cases by using pairwise deletion (and you've already screened your data set for erroneous entries), I'd wager that one or more linear dependencies among your variables is the cause. Since you're using SPSS, I'd suggest doing the following as a quick and dirty check:

1. Run the regression subprogram, and enter all of your variables as IVs (Independent variables). If your data set has any other variable in it beyond those in the path model, enter it as the DV. If you don't have an extra variable, then create a faux variable by either typing in random values for each case, or using the spss random number generator to create one for you.

2. Be sure to check the box for "collinearity diagnostics" before executing the regression.

3. Now, check the VIF (looking for instances of very high values, e.g., > 10) or tolerance (looking for very low values; they are reciprocals of each other). Variables with unusually high/low values are likely to be the culprits of your problem.

Good luck with your work.

A crude but sometimes useful way is performing factor analysis and ask for the determinant of the covariance/correlation matrix. If this is close to 0, linear dependency could be problematic during estimation. Factoranalysis might also give negative eigenvalues and these may never be negative otherwise the correlation matrix can not be semi-positive definite ( if I remember correctly). Maybe R has a procedure to calculate the rank of the correlation matrix. The difference between the number of variables and the rank of the correlation matrix could indicate how serious the dependencies are. It is a crude manner if you can get the information. But calculating the rank is not easy, so maybe even R does not have a procedure do get the rank of the matrix.

The advice by David Morse is very useful if you want to identify variables that may be linearly dependent.

Using correlation matrices obtained via pairwise deletion often is another reason for non positive definite correlation matrices. Here is the reason why:

The problem with pairwise deletion is, that it can produce correlation matrices that do not satisfy the triangular inequality conditions among triples of correlation coefficients. For an explanation I will draw heavily from Wothke (1993) (see below). The admissible range of correlations between two variables i and j is co-determined by the correlations of all other variables with i and j. Consider the following correlation matrix

     v1 v2 v3

v1 1.0

v2 .9 1.0

v3 -.5 .9 1.0

V2 correlates .9 with both variables v1 and v3, which, in turn, are correlated at -.5. However, if r(v1,v2) and r(v2,v3) are taken to be .9, r(v1,v3) can range only between .62 and 1.0.

You can check the admissible range by calculating the limiting values of r(vi,vj) using:

limit1 = cos(acos(vi,vx)-acos(vj,vx))

and

limit2 = cos(acos(vi,vx)+acos(vj,vx))

where x stands for any arbitrary third variable in the same correlation matrix. In the example, the range of r(v1,v3) is limited between

cos(acos(.9)-acos(.9)) = cos(.451 - .451) = 1.0

and

cos(acos(.9)-acos(.9)) = cos(.451 + .451) = .62.

If, due to pairwise deletion of missing values, r(v1,v3) happens to fall outside these limits, the correlation matrix is not positive definite, that is, at least one eigenvalue is negative. The above correlation matrix yields the following eigenvalues:

( 2.047, 1.500, -.547)

As a consequence, a procedure using this correlation matrix will stop with the warning: Matrix not positive definite.

For a more detailled discussion see:

Wothke, W. (1993). Nonpositive definite matrices in structural modeling. In K.A. Bollen & J.S. Long (Eds.), Testing structural equation models (pp. 256-293). Newbury Park, CA: Sage.

Thank you David Morse Dirk Enzmann Peter Moorer .

I was able to finally run an analysis on AMOS by removing from the above model security/perceived risk and just leaving th 'overall risk' variable.

However, I have a low fit of my data to the model, and given time contrasts I doubt I would be able to double the number of data I got (I only have 217 responses..).

What could I do? At the moment I have a

- CMIN/DF: 18,5

-CFI: 0,46

-RMSEA: 0,285

I tried to go through the modification indices, but the only available covariance modification i could do between two 'errors' doesn't make sense and would only improve my model by 4,7.

Any suggestions?

Hello Clotilde,

What might the poor fit indices suggest?

1. The model is misspecified. This can arise from including variables that don't need to be in the model and/or by excluding important variables that should be in the model.

2. The measures you use are poor. This could be due to low reliability (high measurement error), poor validity, or both.

3. There really isn't a linkage among the variables you're considering for the model under evaluation.

4. Your sample is peculiar in some special way(s). This could include features such as: not being representative of target population; misunderstanding directions; willful "Christmas treeing" or fanciful responses.

5. Some combination of these.

I don't think it's sample size that is the problem. Sometimes, a given model, no matter how thoughtfully developed, just doesn't work well to explain the relationships in a data set.

Thank you David Morse . Attached you find the pictures I was trying to upload yesterday.

What would you suggest doing? :( I have to hand in my thesis end of August I am not sure what the best strategy is now then

here

Dear David Morse Clotilde Zanon

From my personal experience, after computing the observed variables we get low model fit for SEM. Several times, when I have run the measurement model I got acceptable model fit, whereas after imputing and running the imputed variables in SEM, the model fit indices weren't in acceptable range. Thus, personally I prefer to run SEM by measurement variables.

Hello Clotilde,

I would simply report that the proposed model fared poorly in accounting for the relationships observed in the data set. I would look specifically at standardized residuals to determine which relationships were least well accounted for (bigger residual = poorer fit). It's fair to mention the possibilities I listed earlier as potential reasons for the overall model performance.

However, with your insight into the variables, the genesis of the model under consideration, and your sample, you may be in a pretty good position to make educated guess(es) as to what the next research step(s) ought to be for those who would follow in your path. That's potentially more helpful than figuratively throwing up your hands and saying, "Further research is needed!"

Good luck with your defense.