# Exploratory factor analysis and latent variable measuring actual use

I have a technology acceptance model where I assume that 10 independent variables (each latent variable is composed of three items, based on a 1-5 likert scale) should influence the actual use (dependent variable) of a contactless payment system. Only the dependent variable is composed of two items, the first one measure the frequency on a 1-5 likert scale (1.never - 2. few times per year - 3. few times per month - 4. few times per week - 5. every day) while the second one measure the number of uses (so it is an open ended question, linked to the previous item).

I need to conduct a SEM analysis so I should start with an exploratory factor analysis.

My sample is composed of 350 cases and I've found that for the two items measuring actual use the distributions are strictly not normal. In particular, only 48% declared to use the system and usage ranged from 1 to 730 per user over a period of one year. The first item has a Skewness of 1,535 and a Kurtosis of 2,180 and the second item has a Skewness of 6,934 and a Kurtosis of 54,817.

So I would like to ask if it is possible to conduct the analysis. Should I first standardize all the variables, because of the different scales of measure, and then transform both the two actual use variables to normalize the distributions?

Thank you so much, it is for my thesis and I have big big troubles

• To me, it does not make much sense to model your DV as a latent variable measured by two indicators. I'd only use one and choose the more informative one. This should be sufficient and reduce unnecessary complexity. – hplieninger Aug 15 '13 at 11:50

## 1 Answer

If I understand correctly, then there are two reasons, why doing an EFA does not make sense in your case. EFA is an exploratory method that is used to find out how many latent factors there are in a given dataset. But for one, you not only want to find the number of factors. You want to find out wether one set of variables are associated with another variable. The second reason is, that you already know how many latent variables you have. So you need to take a structural equation modelling (SEM) approach.

Having that said, I don't see a reason why you should not conduct the analysis. The only thing that might be a problem is that your sample size ends up being too small for such a big model. You have 10 latent independent variables (which by the way are also called exogenous variables in SEM), measured by 3 items each, correct? The first thing that you should do, is to test the measurement models for your latent variables. Basically this means performing a confirmatory factor analysis for each latent variable. If it turns out that, say, for one of the exogenous variables the three items don't actually measure the same construct, then it does not make sense to incorporate this latent variable in further analysis.

I would not standardize the variables before conducting the analysis. I don't have a reference here, but it can make a difference wether you use covariance vs. correlation matrices in factor analyses. And you don't want to lose the additional information that is in the covariance matrices. The only place where that seems to be a problem anyway is in the measurement model of the dependent variable. But you should be able to accomodate for that by specifying a $\tau$-congeneric measurement model. However, if someone else has a better argument in favor of standardizing, I'd be interested to learn more.

Once you have established the measurement models for the latent variables you can do the SEM analysis for the association between the exogenous variables and the dependent variable (wich is also called an endogenous variable in SEM). I hope this helps.

• Just to add to this answer -- you should model these complicated variables explicitly as an ordinal and as a Poisson within the context of the generalized latent variable models that allow GLM-type links. – StasK Aug 15 '13 at 12:27