Negative values in a Pattern Matrix after Exploratory Factor Analysis

#1
Hi,

I've run an EFA (Principle Axis Factoring) with an Direct Oblimin rotation to pilot some scale items.
I have two cleanly loading factors in the Pattern Matrix (confirmed by Scree plot and Monte Carlo). Alpha is high for both.
However -
The first factor only has positive values, the second factor only has negative values.
All the items loading on the first factor were negatively worded, all the items on the second were positively worded ( I did remember to reverse score).
None of my text-books mention what negative loadings mean!
Can anyone help me with how to interpret please?
 

spunky

Doesn't actually exist
#2
(confirmed by Scree plot and Monte Carlo)
Care to elaborate on what this "Monte Carlo" is? Is this Horn's Parallel Analysis?

The first factor only has positive values, the second factor only has negative values.
All the items loading on the first factor were negatively worded, all the items on the second were positively worded ( I did remember to reverse score).
This is weird because it honestly reads like a classic case of "oops, forgot to reverse code". If you run (corrected) item-total correlations treating each factor as an independent subscale, do you observe more or less the same pattern of negative correlations? And are the loadings like close to 0 and negative or are they large and negative?
 
#3
Care to elaborate on what this "Monte Carlo" is? Is this Horn's Parallel Analysis?



This is weird because it honestly reads like a classic case of "oops, forgot to reverse code". If you run (corrected) item-total correlations treating each factor as an independent subscale, do you observe more or less the same pattern of negative correlations? And are the loadings like close to 0 and negative or are they large and negative?
Thanks for the reply Spunky,

Yes Monte Carlo is Horn's Parallel Analysis.
And yes, when I first saw it I thought I had made a coding error. Still hoping I have to be honest, will triple check...

As it stands at the moment my values on factor 1 range from 0.50 to 0.82, and on factor 2 range 0.45 to 0.85

Item-total correlations were calculated when I ran alpha on each one right? The 'Corrected Item-Total Correlations' have no negative values.
 

spunky

Doesn't actually exist
#4
Item-total correlations were calculated when I ran alpha on each one right? The 'Corrected Item-Total Correlations' have no negative values.
No. Corrected item-total correlations are.... well, that. You get the column of each item and correlate it with each sum score or average score or whatever way you're creating a 'score' in your scale. And they are "corrected" because the total score is calculated without the item you're correlating. Otherwise you'd inflate the correlation because you're essentially correlating the item with part of itself. Alpha is the average item covariance divided by the total variance of the scale and it is theoretically bounded by [0,1]. If you had a negative alpha, you'd be in trouble.

Item-total correlations provide an approximate bound to what the loading of a factor is. That's what people used to do back in the days of Classical Test Theory before latent variable models came around. They're still pretty useful to diagnose factor models because those are finicky whereas item-total correlations are fairly stable.

BTW, which software are you using to do these analyses? (please don't say SPSS :p)
 
#5
Hi there,

Negative loadings can mean a few things. First, you should consider whether or not the questions make sense and are theoretically grounded and you can justify keeping the question(s) in the final scale. Sometimes questions can take away from the overall scale and 'make things worse' so to speak. If your factor with negative values has less than 3 items on it, I would remove the scale (check your eigenvalues and all other appropriate statistics before, but generally a good rule of thumb is if your scale has 3 items or less it doesn't contribute that much to the grand scheme of things).

Second, and what may be a better option for you, is that the questions need to be reverse scored in the final measure. If your negatively-worded questions are giving you a negative value when you reverse score them I would encourage you to step back first. As factor analysis is statistically driven and your initial wording and working theory is not, I would recommend running EFA or PCA on the data prior to doing any recoding or negative coding on any of the data. When you have the results from the analysis you can determine if the questions are supposed to be reverse scored or not.

Example: A 10-item measure, you run PCA. You get 10 factors (expected), but only the first 3 have eigenvalues above 1.0. Factor 1 has weights of .386 - .586, factor 3 has weights of -.389 through -.876, and factor three has 4 items with weights of .580 - .678. Keeping in mind the balance/greatest weight of the item is the factor to which it applies, read over the data. The items in factor 2 may need to be reverse scored. Try reverse scoring the items on factor 2 and then run a confirmatory factor analysis and determine the results.

Food for thought: I ran in to this issue multiple times (more than I should ever care to admit publicly....) when I was making a new measure for a construct that consisted of 45 items. What I did was run principal components analysis (PCA, which is different from factor analysis) and determine the number of latent variables I had. I kept anything that had eigenvalues above .7 and any item(s) with a weight of less than .300 were discarded. After running the PCA I ran a confirmatory factor analysis (CFA). PCA asks 'What is the underlying structure I have here?', which in my case PCA said 'You have 3 factors that relate to your construct.' CFA says 'Hey, PCA said this. Was he right?', which in my case CFA said 'Yeah, pretty much. Here are the stats to prove it.'

Tip: SPSS doesn't do confirmatory factor analysis. If you are using SPSS I recommend using it for the PCA because the output is much nicer and you can do more rotations in SPSS than you can in other programs (if you need rotations at all). Once you have your underlying factor structure from your PCA run a CFA using Rcmdr. Rcmdr is an R plugin and is completely menu-driven so no coding experience is necessary. The output is very easy to interpret, setting up the analysis is easy, and all of the necessary statistics are given to you when you run the analysis (plus more).

I'd be happy to help if you wish, feel free to message me if you would like.