Use of CATPCA-Generated Object Scores or CATPCA-Based Summated Scale Scores

[Christina Gregory]

Dear List:

I have a mixed dataset generated from a survey, including 8 demographic items (most of which are multiple nominal). I conducted the NLPCA via CATPCA and have a 5-dimension solution, and thus, five object scores. I am conducting a study in an area in which theory does not yet guide my work, so I am relying on research in which survey research is involved.

In my extensive review of the related NLPCA / CATPCA literature, I am having a hard time discerning the appropriate use of the object (person) scores.  What is a high-level (non-technical) interpretation of object scores? Can the object scores be used in subsequent statistical analyses, e.g., multiple regression, ANOVA? I have a couple of research references that appear to use the object scores in this way. I understand that object scores are standardized scores. Can object scores be viewed as a scale score? I would like to use these new scales as dependent variables (and all explanatory variables are either nominal or multiple nominal).

Also, I developed summated scale scores scales based upon the CATPCA results and tested whether I should use weighted versus unweighted scales (unweighted was what I discovered through correlated the scale scores of both).

My intent was to subject the items from this new survey to PCA, and then use the results to develop scale scores, and then subject these scores to subsequent analyses.  I understand that NLPCA can be interpreted as one would with PCA. From what I've seen, much of the interpretation of the CATPCA results focus on biplots and the like, which is difficult with some of my plots as the object scores are not tightly clustered in some cases.

Any insight would be most appreciated. I've searched this listserv and many other resources and am running out of time.

Christina

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[Kooij, A.J. van der]

Indeed, NLPCA results are to be interpreted like with PCA. The only difference is that interpretation relates to transformed variables instead of the original variables.
Object scores is just alternative terminology for component scores, thus they are weighted summation scores, that is, sum of the (NLPCA: transformed) variables weighted with their loading. The loading being the correlation between the (NLPCA: transformed) variable and the component scores.
So, yes, can be viewed as scale scores, and can be used in subsequent analyses.

The plot of component scores is helpful for checking multivariate outliers. As component scores are standardized scores, you should see a cloud evenly spreading in all directions, within the range of about [-3,3].  A point lying far from the cloud indicates an outlier. With severer outlier(s), you might see most of  the scores tightly clustered and one or some scores far away from this cluster, meaning that those persons are very different from all the others.
 (is this what you mean with "... the object scores are not tightly clustered in some cases."?)
Such a plot indicates that the results are focused on the difference between one or a few persons and all the others. To remedy this, you could delete the outlying person(s). Alternatively, you can partly delete them by setting their values to missing for only the variable(s) causing them to be outliers, and specify missing option Passive (the default: Exclude missing values)  To identify those variable(s)  you look at the loadings plot and relate to the components scores plot or, more conveniently, the biplot of component scores and loadings.

Regards,
Anita van der Kooij,
Leiden SPSS Group, Leiden University

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[Christina Gregory]

Hi Anita:

Thanks for your response.  In fact, I am following your 2012 tutorial as well as the other research generated by your institution/graduates.

I am familiar with linear PCA, but there, it is easy to link summated scale scores with the original scale.

QUESTION
So, with NLPCA,  interpretation relates to the transformed variables...this means that I have to look at the range of values for the transformed variables and interpret based on those values. This means that I am looking at the individual transformed survey items related to the object score, yes?

For example, one of my object scores is based upon 10 items - the original variables reflected the use of a six-point, balanced, Likert-Type Agree-Disagree scale and they load on Component (Object Score) One.  The RANGE across all Object Score One is -1.96 to 3.25. I understand that I can't go back to the Agree Disagree scale.

QUESTION
So, when I'm looking at the Object Scores Biplot, does this mean that my interpretation relies heavily on the values on the x and y axes only within the context of how I've labeled and defined each of the components (dimensions)?

Your explanation makes sense when the object scores tightly clustered. However, I have the case in which the scores are not tightly clustered, in which case, I would say that the two scales (object scores) aren't related to each other......yes?

QUESTION
I'd like to use the object scores in additional analyses beyond examination of plots.  I'd like to be able to say that there are significant differences between groups as well--much of my audience expects this kind of comparison.  It seems that nonparametric statistical analysis is appropriate, e.g., Kruskall Wallis, Chi-Square, but at the same time, shouldn't I be able to use the object scores as dependent variablesin a regression? In my search of the literature, I've had a hard time finding exemplars related to my study/survey research--there are a few, e.g., Lopes, Calapez, & Lopes, 2015; Cascardi, Blank, & Dodani, 2016; Figini, Kenett, & Salini, 2010; Santos, Pizarro, Mota, & Marques, 2013; Vrooman, 2013; Zeijl, te Poel, Dois-Remond, Ravesloot, & Meulman, 2000.

Many thanks for your assistance.

Christina

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