I have a panel dataset with one dependent and twelve independent variables. There are 50 individuals with data for 100 days. Theoretically, most of them should be significant. First, I checked for fixed effects using breusch and pagan lagrangian multiplier test. As I found the fixed effects to be significant, I performed the Huasman test. Finally, I chose random effects model. I am getting at most 4 variables significant using p-value for all models (pooled, fixed, and random). The problem is very low adjusted R-square(0.01 to 0.02). when I use least squares dummy variables model (LSDV) with all days as dummy variables, I find all the days to be significant apart from some explanatory variables and the adjusted square value becomes 0.90 (approx.). Since my days are 100, so there are 100 dummy variables. I also find R-square to be 0.90 when I use individuals' dummy variables (50) in the LSDV model. My questions are:
- Is the difference between RE model and LSDV model R-squares due to the unobserved heterogeneity correlated with all of the regressors in all time periods?
- Is there a limit to include dummy variables?
- Is my LSDV model better than FE model or RE model?
Kindly also guide me to appropriate literature. The analysis is conducted in R using package plm.