query_vars.py

# Examines the effect of changing a single variable
# Takes in the name of the variable, the trace, and the data
def model_effect(query_var, trace, X):
    
    # Variables that do not change
    steady_vars = list(X.columns)
    steady_vars.remove(query_var)
    
    # Linear Model that estimates a grade based on the value of the query variable 
    # and one sample from the trace
    def lm(value, sample):
        
        # Prediction is the estimate given a value of the query variable
        prediction = sample['Intercept'] + sample[query_var] * value
        
        # Each non-query variable is assumed to be at the median value
        for var in steady_vars:
            
            # Multiply the weight by the median value of the variable
            prediction += sample[var] * X[var].median()
        
        return prediction
    
    figsize(6, 6)
    
    # Find the minimum and maximum values for the range of the query var
    var_min = X[query_var].min()
    var_max = X[query_var].max()
    
    # Plot the estimated grade versus the range of query variable
    pm.plot_posterior_predictive_glm(trace, eval=np.linspace(var_min, var_max, 100), 
                                     lm=lm, samples=100, color='blue', 
                                     alpha = 0.4, lw = 2)
    
    # Plot formatting
    plt.xlabel('%s' % query_var, size = 16)
    plt.ylabel('Grade', size = 16)
    plt.title("Posterior of Grade vs %s" % query_var, size = 18)
    plt.show()