The factor scores form part of the validity (refer to the attached example).

For additional analysis, you could calculate the composite constructs, when conducting the factor analysis in SPSS: in the “Scores” tab select “Save as a variable”, which will create composite (regression) variables in the SPSS data set. These can then be used to conduct regression analysis between the different constructs. You can also use ANOVA or a Generalized Model in SPSS to compare the satisfaction levels of passengers between different groups of passengers. Refer to some good SPSS books in this regard:

Field, A. 2009. Discovering Statistics Using SPSS. 3rd Edition. London: Sage.

Pallant, J. 2010. SPSS Survival Manual. 4th Edition. New York: McGraw-Hill.

I am somewhat confused about what your analysis is. Are the three factors that you created independent variables for a regression equation where satisfaction is the dependent variable?

Sze Yang Lim, using estimated factor scores is an alternative to using sum/mean scores. There are advantages and disadvantages of both of these approaches to creating an index/scale. The point of using factor scores is that all of the variables/items that load (weak and strong) on the factor will be taken into account in the estimation of factor scores. However, in the case of sum/mean scores, only those variables/items that load strongly on the factor will form the sum/mean score. You still should run a factor analysis prior to creating an index/scale using either approach.

David L Morgan, Mehmet Mehmetoglu , Rodney Duffett I have a data set consisting of 14 different variables that measure satisfaction levels for various types of service for an airline - these are the raw scores from more than 20,000 passengers using Likert Scales.

Using PCA and FA, I have extracted 3 factors that can account for all these 14 types of services. I then used the regression method to generate factor scores, so that's 3 factor scores per passenger i.e. FAC1, FAC2, FAC3.

Now, I'm supposed to compare satisfaction levels between different groups of passengers, say, business class vs. economy class. My question is, how can I compare satisfaction levels using factor scores since they are standardized scores or z-scores (i.e. the mean of the factor scores PER factor from the entire data set will be 0 and standard deviation 1). For instance, I cannot run an independent samples t-test to compare factor scores (which as I said, are z-scores) between business class and economy class passengers in terms of their satisfaction levels under FAC1.

My colleague suggested that I sum up the raw scores of the variables under each factor and use that as an "index score." So if FAC1 has 5 statements which rate satisfaction levels for a particular type of service, I sum up the RAW Likert scale score for all 5 statements and take that as the "index score." I can then run an independent samples t-test since there are raw scores.

Another suggestion was to go back to Rotated Component Matrix. In this matrix, under each factor, there are various loadings for the variables associated with each factor. The suggestion was to multiply these loadings by the raw Likert scale scores, and sum them up under each factor to get an index score for each factor per passenger.

However, the 2 methods above don't use the factor scores, which makes me question the relevance of these factor scores here. I also question the validity of these methods.

How exactly can I use these factor scores? I'm not running a regression analysis. I just need to compare satisfaction levels between different types of customers across these 3 factors.

After obtaining the component structure using PCA, you can sum up the scores of those items that loaded on a component to derive the component score. Inter component correlations may guide you whether to obtain a scale score by adding up all the three component scores or not. In either case you can employ a mann Whitney / independent samples t test to compare between two groups.

Dear Sze Yang Lim,

Thank you for sharing a very interesting research question.

My understanding is: if you have two groups of passengers, e.g. business class and economy glass (as you mentioned), it might be that the 14 items may load differently onto the factors (e.g. different number of items per factor, number of factors). If this is the case, this would indicate that passengers of business class and economy class may have different concept/construct about that satisfaction mean to them.

Since you have a large sample (20,000 passengers), you may consider exploring if this is the case. This could be done by disaggregating the data by class (e.g. business and economy) and run the EFA for each group and see if the 14 items load the same way for the three factors for the two class. If it is the same, then you could consider computing the composite score by adding the raw score of the same items per factor to yield the factor scores. Using raw factor score is also straightforward in interpreting the results, particularly when you compare the mean scores for two groups.

In case the items load differently for two classes (in terms of the number of items), you may consider eliminating items with low loadings. It is important that when comparing the satisfaction level between two groups, the factor obtained for these two groups are of the same nature, which is typically indicated in the salient loadings that the factors account for.

From my limited knowledge, factor score (typically used in regression analysis) as they help overcome the issue of multicollinearity, among other benefits. You may consider running a CFA after the EFA.

All the best,

Tuan

You can take the analysis further by using some of the techniques of structural equation modelling such as multi-group analysis or multilevel analysis.