# Is it right to estimate the mean of scores obtained from Factor Analysis?

#### IsaMolly

##### New Member

Does it make sense to use the score obtained from a factor analysis to estimate the mean and standard deviation that I present in the descriptive statistic table of my research?

I am working in a research to show how institutional distance affect the performance of Franchises. The institutional distance variable has six dimensions, and each dimension has multiple indicators. I reduced two of these dimensions using factor analysis, and the others dimensions were created by adding the indicators. My question is related to how I should estimate the mean of variables to present them in the descriptive statistics table (see attached file). Each variable has 2,457 observations and I estimated the mean just using the average function in SPSS. However, as you can see in the attached table, the mean of political and cognitive dimension was negative, while the others were positive. One of my reviewers said that a negative mean is not possible, so I am asking for help to clarify this point. I estimated the mean of political and cognitive dimensions with the scores obtained from the factor analysis for each observation (the average of the scores from factor analysis). The media of the other dimensions was the average of the added indicators, for example I added three indicators to create the economic distance. All dimensions created by adding show a positive mean.

#### kiton

##### New Member
Hello there! Let me firstly clarify -- you are saying that "institutional distance variable has six dimensions, and each dimension has multiple indicators". I assume it would be correct to say, the construct of institutional distance is represented by 6 variables (e.g., x1-x6), each of which is measured with multiple indicators -- is this correct? Now, using two different strategies to reduce the dimensions of x1-x6 does not sound like a good idea as it introduces the notion of inconsistent measures and may lead to bias in estimates. Moreover, you would have two different interpretations of the results for each type of the resulting variables.

Furthermore, could you please clarify the following "estimated the mean of [...] with the scores obtained from the factor analysis for each observation (the average of the scores from factor analysis)". Typically, when factor analysis is used to reduce the dimension of the variables, researchers use a resulting factor (or component -- depending on type of the analysis) that emerges from the analysis -- is this what you were using? Note, factor analysis is not as simple as it may seem -- there is a need for strong theory and empirical support for each factor.

Also, note that although the sign for the factors is indeed negative, I'd rather say it revolves around the mean of zero, instead of making an accent of the negative sign. This is common for the factors.

As such, to keep things simple I would use the summation of the indicators first and then explore the consistency and plausibility of the estimates.

#### IsaMolly

##### New Member
Kiton,

It's correct your interpretation that “the construct of institutional distance is represented by 6 variables, each of which is measured by multiple indicators.” You shed some light when said that using different strategies to reduce the dimensions is not a good idea. Surprising, the reviewer did not say something about that, but I will review my strategy and see what happen when I use either addition or factor analysis.

Related to using factor analysis, I understand your concern. In my case, I applied factor analysis to multiple indicators of the political and cognitive distance, and I obtained that just the first factor explains more than 80% of the variance. As a consequence, I am using only one factor to measure political distance, and one for cognitive distance.

Related to what I am using to estimate the mean, it is not the component from factor analysis, but the factor scores I obtained from SPSS (see attachment 1). When you perform a factor analysis in SPSS, the software gives you the option of saving the factor scores as a variable (see attachment 2). As a result, I obtained a new variable in my dataset with 2457 observation, the exact number of observation that I have for the original values. I estimated the mean of this values.

Thank you

#### kiton

##### New Member
Kiton,

It's correct your interpretation that “the construct of institutional distance is represented by 6 variables, each of which is measured by multiple indicators.” You shed some light when said that using different strategies to reduce the dimensions is not a good idea. Surprising, the reviewer did not say something about that, but I will review my strategy and see what happen when I use either addition or factor analysis.
Good, try both approaches and see how your model "behaves".

Related to using factor analysis, I understand your concern. In my case, I applied factor analysis to multiple indicators of the political and cognitive distance, and I obtained that just the first factor explains more than 80% of the variance. As a consequence, I am using only one factor to measure political distance, and one for cognitive distance.

Related to what I am using to estimate the mean, it is not the component from factor analysis, but the factor scores I obtained from SPSS (see attachment 1). When you perform a factor analysis in SPSS, the software gives you the option of saving the factor scores as a variable (see attachment 2). As a result, I obtained a new variable in my dataset with 2457 observation, the exact number of observation that I have for the original values. I estimated the mean of this values.
Ok, we are on the same page here -- the saved factors scores are simply referred to as factor (or component in case of PCA), I was just confused by the "means" interpretation.

Let me ask you this though. As I haven't come across "institutional distance", why is it measured with 6 variables? Are these variables correlated (assuming it may bias your estimates, if there are highly correlated)?

#### IsaMolly

##### New Member
Yes, they are highly correlated, the person correlation oscillate between .78 and .85
The reason to have 6 variable to measures institutional distance is theoretical. Previous studies have showed that the construct is multidimensional.

#### kiton

##### New Member
In such case, I would suggest to run a factor analysis on (A) six dimensions, and (B) on all indicators. Then using scree plots examine and compare the results.

Note, for most models you'll need assumption of lack of multicollinearity to hold. When identifying factors, pay attention to the number of those with eigenvalue > 1. Assuming, you have, say, 2-3 of such distinct factors --> save them, check the correlation -- it might drop (ideally it should, assuming you have found quite distinctive dimensions).

If your goal is to explore the dimensions constituting the construct of interest using data in hand (and thus make a contribution), there is a variety of funky stuff that can be done with factor (or component) analyses, establishing validity, reliability, etc.

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#### dungdn93

##### New Member
That is correct your interpretation that "the structure of the institutional gap is represented by six variables, each of which is measured by the indicators." You clarified to say that the use of different strategies to reduce the size is not a good idea. Normally, when the factor analysis was used to reduce the size of the variables, the researchers used an element results (or component - depending on the type of analysis) that emerged from the analysis - is what you are using