The way you explained it screams "Overfitting" loudly. By having too many variables, your model will have high R² but low AIC. This assumes that those variables are not collinear (typically occurs when having too many dummies) or almost collinear (driving the condition number kappa of your matrix extremely bad). Furthermore, there are also some issues regarding the number of data points you have. The more variables you want to include, the more data points you will need. Having at least 35 data points is the minimum, but the regression would be extremely unrobust.

Hi Christopher,

I suggest that you try first of all a data analysis by such as Principal Component Analysis. and after you may use regression step by step.

The optimum number of variables depend on efficiency - variance trade off. So, it depends on your priority. I would suggest create indices by putting together similar variables (PCA is definitely one of them as suggested by Jamel).

You should perform the multicolinearity test or/and to check the correlations between independent variables and if there is a correlation between two of them which is over 0.85 you should consider to get rid of some independent variables.

I think if some of the variables are related, you can reduce the number by creating index for some of them (using principal component analysis- PCA). But check the multicollinearity among the variables to ensure they are high before using the pca.

Thank you

Even if you can get rid of the interdependence of the explaining variables, there remains the problem that a well-being-index cannot be a really exact measure. I thinkg there will be anly a small number of marks (like for school marks) and they will be far from usual scales. Nevertheless, you may try an analysis with all your independent data just for fun (if you have enough observations). If you try to interpret the results, I am sure, you will find that they are senseless.

One always has to be concerned about the number of so-called independent variables used in explaining a dependent variable and that's why we typically report the "degrees of freedom' which are reduced by as you include more independent variables in an explanatory model, so the fewer the degrees of freedom one has, the less reliable is the model as a predictor or explanation often expressed as power of a test. The strategy of including all your presumed independent variables and then dropping those that add little or no explanatory power to the model is generally frowned upon by theorists and those who see testing the model's ability to explain or predict, but this strategy may be deemed acceptable if one is primarily interested in predicting the dependent variable's magnitude. Factor analysis is a statistical methodology that can enable one to discover how several independent variables are related one to another and thence to the dependent variable. You may want to refer to some of my work done in the 1970s and in an article I published in 2002 for a general description of the technique and its application to socioeconomic data analysis. Of course there are many other sources you can find. Sociologists and psychologists have developed employed factor analysis in much of their quantitative analysis over the decades, economists much less so. Refer to a good text on multivariate analysis and analysis of variance for technical treatments and use of the techniques appropriate for handling the kind of data you are using. A early seminal contributor to the collection of techniques comprising factor analysis and principal component analysis was the late Louis Leon Thurstone at University of Chicago in psychometrics. See also Harry H. Harman of Chicago, Modern Factor Analysis.

The role of discretion and judgment, both of which are needed in using factor analysis have created controversy and militated against its widespread use, however, with rise of "Big Data" we may yet see it put to more general use in data analysis.

The "degrees of freedom" may not be a problem, if one has a lot of obserbations. Nevertheless, it is not reasonable - I would even say: forbidden - to run regressions with interdependent explaining variables. Therefore, applying factor analysis is a good proposal. Maybe, one could use its results to construct equations which can be tested/estimated by ususal econometric methods.

You have many independent variables: To check the multicollinearity among the variables use the Variance Inflation factors.

First to use 35 independent variables your observations need to be above 70, use Principal Components Factor or analysis to determine the variables rank on the dependent variable.

Use multicollinearity to remove variables with correlation of above 0.70.

After those two criterias, add the best variables based PCA and other variables gradually watching your adjusted R-square. Discard variables that reduces the adjusted R-SQUARE drastically while still increasing the R- square.

You can use LASSO, Ridge regression or Elastic net regression if your problem is overfit. You could use data reduction also (principal components) but principal components make sense if you could associate some socioeconomic reasoning for each component uses. But to do that I prefer to run structural equation models with latten variables. You can do all of that with stata.

Hi everyone! Thank you a lot. You gave the essential insigths. However, I have to tell you that my sample size is n=28 000 (it's a national survey). With all the non responses, N/A, etc. for each question I still have, in the worst variable, a n=2500, which is more than 70 observations per parameter. Is it still a problem even with that sample size? What other considerations do I have to take into account (apart from the multicolinearity as I already did it testing the VIF)?

Tonuchi Emmanuel Joseph Horst Rottmann Anton Rainer Oscar Travis Brookins Samuel Tawiah Baidoo Goran Miladinov Basab Dasgupta Jamel Henchiri Jamel Henchiri Leonardo Oliveira

Hi Santiago. Maybe you can also try testing Multiple Linear restrictions using Wald test. In your specific case you can test which of your independent variables have jointly significant effect on your dependent variable.Thus, according to your specific research interest then you should conclude which of the variables (where you could find a joint significance) to drop i.e. which ones are redundant in your research case. I hope this is helpful for you.

Good luck!

You also need to be careful about "bad regressors". Bad regressors create endogeneity by measurement problems, simultaneity or other froms of correlation with the erros.