I am currently trying to create a scale to measure a multi-dimensional parenting construct. There is currently no strongly established theory about the construct and I am investigating it in an age group that has not typically been the focus of parenting researchers. I created a list of 26 items based on a qualitative study and have done an EFA on the data. Almost half of the items are skewed and some are quite kurtotic due to low base rates of those parenting behaviours. However, I believe that these items are theoretically relevant to the construct of interest. Due to high skew/kurtosis/presence of non-normality, I used polychoric correlations for the EFA. A 3 factor solution was recommended.
My questions are:
1) The determinant of the matrix is less than .00001 but Bartlett's and KMO are good (fit indices are generally good as well). I have read in previous discussions online that
you can eliminate the atypical values by using the mahalanobis distance, in values of .000. For EFA you must use ordinary or generalized least squares analysis in oblique rotation since you refer that it presents several factors, although it is taken more into account what you refer of asymmetry and kurtosis for the estimation in CFA model, the communality is taken into account before seeing the factorial loads.
Hello Vivien,
First, very small determinants imply a lot of redundancy within the variable set (collinearity). Normally, that's a good thing if you think that the variables should work jointly to reflect some latent construct/s. Could it be exacerbated by sharply skewed data (e.g., lots of zero or lowest scores)? Yes. How sharply does that threaten the utility of a factor analysis? Less than you might think.
Second, loadings can and frequently are higher than communalities, because loadings are ordinary correlations (variable-factor) and communalities are analogs of squared correlations (e.g., variance accounted for, or shared variance). So, the upper limit for a loading would be on the order of the square root of the communality (for example, communality of .4 implies maximum loading of about .63 in a simple structure model).
Finally, it might make sense to consider an IRT (item response theory) framework, which can be uni- or multi-dimensional in form, as a way to understand better how the variables you've proposed do or don't work together in a coherent manner.
Good luck with your work.
Vivien So, I strongly suspect that David Morse has given you some good advice above. I hope I can add some things that are helpful.
First, are you sure that you have three factors in your data? (How did you determine that? Did you, for example, use parallel analysis?) Second, perhaps check the % of variance accounted for by your retained factors. Ideally that should be up around 60%, and down below around 45% is a bit dodgy. Also, I recommend that, if you do remove items, you do so carefully, perhaps even one at a time, in case only a small number of items are problematic.
I think it helps to explore the specificity of the items within the "potential" factors (dimensions). That is, conduct a bifactor- ESEM and use the bifactor statistics to evaluate the extent to which the set of items load on each proposed factor (i.e., the items are relevant to the factor/dimension) and the general factor (i.e., non-specific, general). A target rotation could be considered as well. Good luck with your project.
Vivien So... One of the very important aspects of scale development is the sample size. You need to have to adequate sample size to perform EFA analysis, otherwise, problems like skewness and kurtosis will appear. Further, in your study (as it is exploratory in nature), you can initially retain items with low commonalities (
As mentioned by David Rasch models can contribute to evaluate the dimensionality of the instrument.
Cristian Ramos-Vera David Morse Robert Trevethan Augustine Osman Sayoni S.
Thank you very much for your help and input. I appreciate it. As follow-up information for our discussion and for any others who may be reading this thread, I did use parallel analysis in EFA and my sample size is around 170 (long story short, I have data for mothers' parenting n=270 and fathers parenting n=196, but wanted to have a factor model that enabled mother-father comparisons, and followed suggestions to use a split-half dataset for EFA with half of the data being mothers' data and half fathers' data, randomly chosen, which left me with 170 after missing data was omitted). The sample size is on the low side and thus will be acknowledged as a limitation. The % of variance accounted for by the factors using the split half dataset is between 50%-60%. I omitted any items that had very low communality (they also happened to be the ones that had double loadings or no loadings above .4).
Vivien So, thank you for your feedback. I regard it as a nice little bit of courtesy on your part.
You seem to be progressing nicely with your research. May things remain that way for you!
Vivian So, one of the uses of the PCA is in creation of new variables. This is because of the perpendicularity of the component/dimensions which ensures elimination of correlation between any two components.
I suggest that you run a PCA up to the factor score output stage, and then use the final variances to eliminate the very low components. Use of initial factor loadings and communalllities to elominiate otherwise valuable research variables is not advisable.
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