The simplest approach would be to calculate coefficient alpha for the three variables, and if it is high enough (preferably above .8), then you can just add the variables (or you can take an average, which is technically the same because you are dividing by a constant).

The main reason for doing a factor analysis would be if the three items have substantially different loadings.

Hello Gjergji Josifi I think the idea you have, that is

and have 3 Likert scale variables which are correlated and seem to represent one thing namely "Attitude towards immigrants"

test in a regression model.

To do this, calculate Collinearity Statistics.

The explanation that collinearity is one of the topics related to the intertwining of the independent quantities of X in each other and their redundancy. The short explanation is that collinearity means there is a strong relationship and high correlation among the X's of the model. Although collinearity exists in all regression models, its severity is considered a shortcoming. Because when two or more X have high collinearity with each other, it is no longer necessary to include all of them in the regression model and they are redundant.

To calculate Collinearity Statistics, you can get the following results.

Variance Inflation Factor (VIF)

Collinearity is measured by a statistic called Variance Inflation Factor (VIF). The size of VIFs shows how much the variance of the estimated regression coefficient increases as the quantities are correlated with each other.

If the VIF is close to one, there is no collinearity between that X and the other quantities, but if the VIFs are greater than one, there is collinearity between that X and the other quantities.

Tolerance

The obtained numbers for Tolerance show that if that X has the role of Y in a regression model and then we establish a regression model between that X that has become Y and other Xs, then the coefficient of determination of R Square is How much will the regression model be?

In this context, the following relationship is established.

Tolerance = 1- R square

In regression models, it is desirable that there is no collinearity between X's and that VIF sizes are close to one and Tolerance is around zero.

If you are interested in this field, see the link below.

https://graphpad.ir/collinearity-diagnostics-spss/

Abolfazl Ghoodjani , David L Morgan thank you both for your answers. David L Morgan what do you mean by 'substantially different loadings'. What if the factor loadings are close to 1 for two of the variables and close to -1 for the other one. Would that be a case where i should use factor analysis since they are substantially different? Another question: Would alpha still make sense if the variables are scale differently? one 7 point Likert scale and the other two 5-point Likert scale

I think the only way that you could get the pattern you describe is if one of your variables is "reversed." If so, then you need to recode it before you add the three together. The 7-point versus 5-point difference does not matter for alpha, because it is based on correlations.

Gjergji Josifi suggestions all apply to the case where you add all three variables as independent variables in a single equation, which I would not recommend for this case, where it seems likely that you can create a single scale variable.

Usually in such situation the variables are added and if the range became very large then the values are merged together in orderly fashion to make theme shorter.

I realize that i should not have recommended simple addition for creating the scale (I only meant that this was not necessary for coefficient alpha). So, before creating the scale you need to standardize each of the variables (to a mean of zero and a standard deviation of one). If you don't do that, the 7-point variable will have more influence than the 5-point variables.

Combining three Likert scale variables that represent a single concept into one factor for use in panel regression involves a process known as factor analysis or a similar technique that allows you to create a composite score or index. Factor analysis is a statistical method used to identify underlying factors or dimensions that explain the correlations among observed variables. Here's a step-by-step guide:

Step 1: Data Preparation: Ensure Data Quality: Verify that the Likert scale variables are reliable and have a sufficient number of respondents.

Step 2: Choose Factor Analysis Technique: Select Factor Analysis Method: Common factor analysis or principal component analysis (PCA) are commonly used for this purpose. Principal component analysis is more straightforward, while common factor analysis assumes that there are underlying latent factors causing the observed correlations.

Step 3: Run Factor Analysis: Choose Software: Use statistical software such as R, Python (with libraries like scikit-learn or stats models), SPSS, or SAS. Specify Model: Define the number of factors to extract (in your case, you may want to specify one factor), and choose the method (common factor analysis or PCA). Interpret Results: Examine factor loadings to identify which items are strongly associated with the factor. Loadings represent the strength and direction of the relationship between the variable and the factor.

Step 4: Compute Factor Scores: Calculate Factor Scores: Once the factor analysis is complete, compute factor scores for each respondent. Factor scores represent the individual's position on the underlying factor.

Step 5: Panel Regression: Include Factor Scores in Regression Model: Use the computed factor scores as the dependent variable in your panel regression model. Other relevant independent variables can be included as usual.

Shiva Dutta Chapagai Is it you or AI that is offering this advice?

David L Morgan It’s apparently AI-generated response.

As I understand, you are trying to merge 3 variables into 1 variable in order to perform a panel regression. Have you collected these data on a questionnaire with likert scale over a period of time (same subjects over multiple years)? If so why would you choose to perform a panel regression?

Anyways, merging the variables as you propose will lead to information loss. Original data represents scale data and merging these variables would mean getting an average value for the variable. This is one way to dot it assuming you have met reliability and validity conditions. As said this will lead to information loss. Why cant use the 3 variables separately? Or the Variable was design in such way to have multi-dimensions?

The purpose of factor analysis is to identify either factors or reduce dimensions. I am not sure how this will serve your purpose. But factor analysis can provide evidence for reliability and validity of constructs. Also you may save factor weights to perform regression subsequently.