Hello Dears;
There are about 70 items and 30 cases in my research study in order to use in Factor Analysis in SPSS. There is an error: correlation matrix is not positive definite. What can I do about that?
I changed 5-point likert scale to 10-point likert scale. I increased the number of cases to 90. But did not work. Hope you have the suggestions.
Best regards;
Dashtpeyma
One obvious suggestion is to increase the sample size because you have around 70 items but only 90 cases. Also, there might be perfect linear correlations between some variables--you can delete one of the perfectly correlated two items. This is a slim chance in your case but there might be a large proportion of missing data in your dataset. Overall, the first thing you should do is to use a larger dataset. You can check the following source for further info on FA: Chapter Exploratory Factor Analysis and Principal Components Analysis
Dear Mosayeb Dashtpeyma ,
I'm guessing than non-positive definite matrices are connected with multicollinearity. Have you run a bivariate correlation on all your items? You should remove one from any pair with correlation coefficient > 0.8. Talip is also right: you need more cases than items. In fact, some textbooks recommend a ratio of at least 10:1.
NPD is evident when some of your eigenvalues is less than or equal to zero. Also, multicollinearity from person covariance matrix can caused NPD.
1. Increase sample size. When you measure latent constructs using multiple items, your minimum sample size is 100.
2. Check the pisdibikity of multiple data entry from the same respondent since this will create linearly dependent data.
Please check whether the data is adequate. Then, the sample represents the whole population, or is it merely purpose sampling.
Thank you so much Khristian Edi Nugroho Soebandrija
it represents whole population. But there are lots of papers working by small sample size (less than 50).
There are some basic requirements for under taking exploratory factor analysis. Sample adequacy is of them. And as suggested in extant literature (Cohen and Morrison, 2007, Hair et al., 2010) sample of 150 and 200 is regarded adequate. I therefore suggest that for the purpose of your analysis (EFA) and robustness in your output kindly add up to your sample size.
the data presented does indeed show negative behavior, observations need to be added to a certain amount, or variable behavior may indeed be negative.
As others have noted, the number of cases should exceed the number of variables by at least 5 to 1 for FA; better yet, 10 to 1. Maybe you can group the variables, on theoretical or other a-priori grounds, into subsets and factor analyze each subset separately, so that each separate analysis has few enough variables to meet at least the 5 to 1 criterion.
Think of it this way: if you had only 2 cases, the correlation between any two variables would be r=1.0 (because the 2 points in the scatterplot perfectly determine a straight line). If you had only 3 cases, the multiple correlation predicting any one of three variables from the other two variables would be R=1.0 (because the 3 points in the 3-D scatterplot perfectly determine the regression plane). With 70 variables and only 30 (or even 90) cases, the bivariate correlations between pairs of variables might all be fairly modest, and yet the multiple correlation predicting any one variable from all of the others could easily be R=1.0. So you could well have multivariate multicollinearity (and therefore a NPD matrix), even if you don't have any evidence of bivariate collinearity.
On the NPD issue, specifically -- another common reason for this is if you analyze a correlation matrix that has been compiled using pairwise deletion of missing cases, rather than listwise deletion. With listwise deletion, every correlation is based on exactly the same set of cases (namely, those with non-missing data on all of the variables in the entire analysis). With pairwise deletion, each correlation can be based on a different subset of cases (namely, those with non-missing data on just the two variables involved in any one correlation coefficient). Pairwise deletion can therefore produce combinations of correlations that would be mathematically and empirically impossible if there were no missing data at all. The result can be a NPD correlation matrix. Did you use pairwise deletion to construct the matrix? If so, try listwise deletion. If that drops the number of cases for analysis too low, you might have to drop from your analysis the variables with the most missing data, or those with the most atypical patterns of missing data (and therefore the greatest impact on deleting cases by listwise deletion).
Do you have positive values only?
Do you have zeros?
Do you have "one column" with all the values equal (minimal or maximal possible values)?
It the problem is 1 or 2: delete the columns (measurements) you don't need
If the problem is 3: delete them as well
70x30 is fine, you can extract up to 2n+1 components, and in reality there will be no more than 5.
On my blog, I covered 4 questions from RG. If you are new in PCA - it could be worth reading: https://www.steemstem.io/#!/@alexs1320/answering-4-rg-quest
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