# Social-Network Peer Effect Regression Analysis

I have locally transformed model from Bramoullé 2009 to be estimated for regression estimation $$\begin{equation} ( \mathrm{{I}} - {G}_{l}^{*}){y}_{l} = \beta_2( \mathrm{{I}} - {G}_{l}^{*}) {G}_{l}^{*}{y}_{l} + \gamma( \mathrm{{I}} - {G}_{l}^{*}){ X}_{l} +\phi ( \mathrm{{I}} - {G}_{l}^{*}) {G}_{l}^{*}{X}_{l} + (\mathrm{{I}} - {G}_{l}^{*}) \epsilon_l \end{equation}$$

Where "I" is block diagonal identity matrix and '$$G^*$$" is block diagonal of the normalised adjacency matrix representing friendship network at the classroom level. Y is GPA and X is some exogenous variable. So 'GY' is the average GPA of all the friends of an individual and GX is the average contextual effect of the friends. GY by definition is endogenous therefore theory suggest$$G^2X$$ which represent friends' friend characteristic can be used as IV for GY. I am using 2SLS for my regression analysis.

My question is for exploratory data analysis such as Scatter Plot shall I use Y and GY or shall I use transformed variable $$( \mathrm{{I}} - {G}_{l}^{*}){y}_{l}$$and $$( \mathrm{{I}} - {G}_{l}^{*}) {G}_{l}^{*}{y}_{l}$$. When I use Y and GY there are 20 outliers at 0. GPA value is between 0 to 4 and I have 2800 obsevation. If I take log(GY) to get rid of outlier then $$( \mathrm{{I}} - {G}_{l}^{*}) log({G}_{l}^{*}{y}_{l})$$ results in NaN value in MATLAB.

And when I Scatter plot $$( \mathrm{{I}} - {G}_{l}^{*}){y}_{l}$$and $$( \mathrm{{I}} - {G}_{l}^{*}) {G}_{l}^{*}{y}_{l}$$. The graph is very messy! So what shall I do?