Exploratory Factor Analysis with dichotomous data "Heywood Case"

[Wendy Ochoa]

Hello,

I'm currently working with dichotomous variables that belong to a 15-item questionnaire that asks participants whether they perceive something to be a barrier to their involvement in school (yes/no). I'm in the process of doing an exploratory factor analysis using Principle Axis Factoring. I was able to calculate the tetrachoric correlation and run my code for EFA after that. However, I get a message on the output that says "Beware: solution is a Heywood case." I was wondering if someone could provide me with some guidance as to why I get this message?

Below is the code I use:

tetrachoric Bar1 Bar2 Bar3 Bar4 Bar5 Bar6 Bar7 Bar8 Bar9 Bar10 Bar11 Bar12 Bar13 Bar14 Bar15, posdef
matrix r = r(Rho)
matrix symeigen e v = r
matrix list v
factormat r, ipf n(194)

Additionally, in trying to determine how many factors I should run, I ran parallel analysis and using the following command:

fapara, factormat reps(10)

However, I do not seem to get a good solution as to how many factors I should run. Below is the graph I get. Does anyone know why I might be getting this output? Do you know of any resources I could use to help me determine how many factors I should run when my data are dichotomous? Any guidance will be much appreciated. Thank you!

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

A Heywood case means that as the maximum likelihood operated, the best solution involved a standard deviation with a negative value (i.e., that is theoretically impossible). Programs often constrain such parameters to be 0 or higher, but this means the maximum likelihood isn't. This does happen in factor analysis.

Normally an exploratory factor analysis gives you information on the desirable number factors. From the graph, it looks like one factor. The parallel analysis is user written - I don't know exactly what it does.

[Wendy Ochoa]

Hi Phil,

Thank you so much for the tips and for your response.

I'm not really sure how to address the Heywood case, do you happen to have any recommendations as to how I can proceed?

Thank you for any advice

[Wendy Ochoa]

I realize that it might be helpful to also copy and paste my code and output:



Thank you!

[Wendy Ochoa]

Codes and output

[Federico Tedeschi]

Do you know of any resources I could use to help me determine how many factors I should run when my data are dichotomous?
[ATTACH=CONFIG]n1519790[/ATTACH]

One could do Principal Component Analysis (PCA), using the cut-off scores of 1 for the eigenvalue (Kaiser criterion).

Does anyone know why I might be getting this output?

My understanding is that "fapara" compares each eigenvalue with the eigenvalue you would get in case the variables were independent. Since this is done by generating a random dataset, one can make several replications (as in your case); it is also possible to use "set seed" to make results replicable. I see the problem with "fapara" similar to the one with factor analysis using an eigenvalue of 0 as cutoff: you retain all factors that are estimates to explain common variance, even if negligible (and even regardless of any statistical significance consideration). In both cases, you may end with many factors that explain very little. I've noticed that, by reducing the number of factors until I get rid of the "Heywood case" warning, I usually end up with the same number of factors as with the Kaiser criterion.