Return to Question

I have a linear model with 6 IVs and would like to analyze the effect of an interaction term applied to all the IVs.

To illustrate, let's say we're predicting the Win/Loose ratio of NBA basketball teams based on a number of players statistics and we want to add the number of spectators coming to the games as an interaction term to all the predictors. The idea is that a higher fans participation in the stadiums will leverage the players skills. Vice-versa if stadiums register low participation (look at the Nets), it will negatively affect the players ability to perform at their best or average levels (side note: we do not want to use the number of spectators as a predictor per se).

In MLR terms the model would be: $$ \hat{Y} = c + b_1X_1 + b_2X_2 + ... + b_nX_n + a_1I_1X_1 + a_2I_2X_2 + ... + a_nI_nX_n$$

Where $X_n$ are the players statistics and $I_n$ is a measure of crowd participation.

If the players skills set (skills IVs) is large, the interaction term will double the model terms, with a higher chance of over-fitting the model data and probably decreasing the predictive ability of the model.

Is there a different methodology that is better designed to adjust the linear coefficients given one or more "background" variables?

I have a linear model with 6 IVs and would like to analyze the effect of an interaction term applied to all the IVs.

To illustrate, let's say we're predicting the Win/Loose ratio of NBA basketball teams based on a number of players statistics and we want to add the number of spectators coming to the games as an interaction term to all the predictors. The idea is that a higher fans participation in the stadiums will leverage the players skills. Vice-versa if stadiums register low participation (look at the Nets), it will negatively affect the players ability to perform at their best or average levels (side note: we do not want to use the number of spectators as a predictor per se).

In MLR terms the model would be: $$ \hat{Y} = c + b_1X_1 + b_2X_2 + ... + b_nX_n + a_1I_1X_1 + a_2I_2X_2 + ... + a_nI_nX_n$$

Where $X_n$ are the players statistics and $I_n$ is a measure of crowd participation.

If the players skills set (skills IVs) is large, the interaction term will double the model terms, with a higher chance of over-fitting the model data and probably decreasing the predictive ability of the model.

Are there other methods than multivariate regression to adjust the linear coefficients given one or more "background" variables? Or is there a way to reduce the number of terms?

I have a linear model with 6 IVs and would like to analyze the effect of an interaction term applied to all the IVs.

To illustrate, let's say we're predicting the Win/Loose ratio of NBA basketball teams based on a number of players statistics and we want to add the number of spectators coming to the games as an interaction term to all the predictors. The idea is that a higher fans participation in the stadiums will leverage the players skills. Vice-versa if stadiums register low participation or are next to empty, it will negatively affect the players ability to perform at their best or average levels (side note: we do not want to use the number of spectators as a predictor per se).

In MLR terms the model would be: $$ \hat{Y} = c + b_1X_1 + b_2X_2 + ... + b_nX_n + a_1I_1X_1 + a_2I_2X_2 + ... + a_nI_nX_n$$

Where $X_n$ are the players statistics and $I_n$ is a measure of crowd participation.

If the players skills set (skills IVs) is large, the interaction term will double the model terms. Is there a different methodology that is better designed to handle this kind of problems?

I have a linear model with 6 IVs and would like to analyze the effect of an interaction term applied to all the IVs.

To illustrate, let's say we're predicting the Win/Loose ratio of NBA basketball teams based on a number of players statistics and we want to add the number of spectators coming to the games as an interaction term to all the predictors. The idea is that a higher fans participation in the stadiums will leverage the players skills. Vice-versa if stadiums register low participation (look at the Nets), it will negatively affect the players ability to perform at their best or average levels (side note: we do not want to use the number of spectators as a predictor per se).

In MLR terms the model would be: $$ \hat{Y} = c + b_1X_1 + b_2X_2 + ... + b_nX_n + a_1I_1X_1 + a_2I_2X_2 + ... + a_nI_nX_n$$

Where $X_n$ are the players statistics and $I_n$ is a measure of crowd participation.

If the players skills set (skills IVs) is large, the interaction term will double the model terms, with a higher chance of over-fitting the model data and probably decreasing the predictive ability of the model. 

Is there a different methodology that is better designed to adjust the linear coefficients given one or more "background" variables?