I have 5 different tests at different levels, all assessing reading, grammar, and vocabulary. However, a different number of students have participated in each test.
For example:
Test 1: 110
Test 2: 120
Test 3: 130
Test 4: 107
Test 5: 109
When I wanted to conduct Exploratory Factor Analysis for the whole dataset, I got a message, "This matrix is not positive definite," from SPSS. That's why the EFA analysis did not work for this dataset. What does it mean? What should I understand from this mistake? How can I solve this problem?
It means your covariance matrix is improper. This can happen when pairwise deletion is used to handle missing data. If this is in fact the reason, it would probably be best to use a more appropriate method for handling missing data such as full information maximum likelihood or multiple imputation.
One would have to look at the details of your data set and analyses. Perhaps there isn't enough data available overall to obtain meaningful factor analytic results.
On an exploratory basis, you could try restricting your analysis to respondents who responded fully to all 5 tests. Alternatively, you could estimate scores for persons who responded incompletely but substantially to enough items on each test. You could base this on imputation or prorating. I've often prorated by dividing scores by the number of items responded to providing the respondent validly answered at least 80% of the items on that test and then multiplying by the number of items on that particular test. (By valid response, I mean any numerical response that is within the prescribed range of individual responses for an item.)
The error "the matrix is not positive definite" occurs when SPSS cannot calculate a valid correlation matrix. This is usually due to not all students taking the same tests (missing data). This distorts statistical calculations, especially correlations. The EFA requires a well-formed correlation matrix without inconsistencies.
Check that all included variables have sufficient variance (no constant values); SPSS will automatically eliminate cases with missing data when performing the EFA. If there are many omissions, consider imputing the data or limiting the analysis to items answered by all.
Three possible solutions:
a. Perform the EFA separately for each test.
b. Combine the tests only if there are common items and students in common.
c. Restructure the database to a "long" format and incorporate a tiered analysis model (advanced option).
The source of this information is GPT Chat. I hope it helps.
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