Hello everyone,
Currently I am estimating the following regression model-
Y_ie = \alpha + \beta T_i + X\delta + \gamma_p + \theta_e + \epsilon_ie ...(1)
where Y is the outcome value of individual i surveyed by enumerator e. \beta is the treatment status of i. X\delta is the vector of covariates. \gamma_p is the program fixed effect and \theta_e is the enumerator fixed effect. Note that each individual i is participant of a specific program. Now, should I include the program subscript in Y_ie and \epsilon_ie? Doing so the regression model becomes-
Y_ipe = \alpha + \beta T_i + X\delta + \gamma_p + \theta_e + \epsilon_ipe ...(2)
Which one is the correct one? model (1) or (2)? It would be helful if you can provide an explanation as well.
Also, I often face difficulties with subscripts in regression models. I know that subscripts represent the dimensions of the data. But in cases with fixed effects (like the ones mentioned above) or clustered standard errors, it gets very confusing for me. Is there any literature on it?
Currently I am estimating the following regression model-
Y_ie = \alpha + \beta T_i + X\delta + \gamma_p + \theta_e + \epsilon_ie ...(1)
where Y is the outcome value of individual i surveyed by enumerator e. \beta is the treatment status of i. X\delta is the vector of covariates. \gamma_p is the program fixed effect and \theta_e is the enumerator fixed effect. Note that each individual i is participant of a specific program. Now, should I include the program subscript in Y_ie and \epsilon_ie? Doing so the regression model becomes-
Y_ipe = \alpha + \beta T_i + X\delta + \gamma_p + \theta_e + \epsilon_ipe ...(2)
Which one is the correct one? model (1) or (2)? It would be helful if you can provide an explanation as well.
Also, I often face difficulties with subscripts in regression models. I know that subscripts represent the dimensions of the data. But in cases with fixed effects (like the ones mentioned above) or clustered standard errors, it gets very confusing for me. Is there any literature on it?
