# What is deviance in lassoglm

I am trying to fit a lasso penalized logistic regression model to a certain data. I am using lassoglm for that in matlab. I use the following function

[B,FitInfo] = lassoglm(X,Y,'binomial','Lambda',0.01,'CV',10);

Using 10 fold cross validation, it will use different samples every time to fit the model. However, I didn't get what deviance means in this case. Lets say for the first run of cross validation, I have k non zero features. For next run, I have a model with m non zero features and so on. What does deviance then measure and how the plot is generated like using that lassoplot. Suggestion?

Actually, I didn't get this figure. What does it specify? ## 2 Answers

According to MATLAB's help, deviance is the value of the loss function for the type of model that you are using. It is the value of negative log-likelihood (MSE for linear regression) for your model averaged over the validation folds in the cross-validation procedure.

According to MATLAB's help, the two points marked in the graph are:

Plots the value of Lambda with minimum cross-validated MSE.

Plots the greatest Lambda that is within one standard error of minimum MSE (so makes the sparsest model within that region).

• And what are the bars for. I mean for each point there is a bar. What is that for? – rajan sthapit Feb 10 '13 at 5:04
• MATLAB's help says: "Plots error bars for the estimates." To me they look like 1-standard deviation confidence intervals. You can see that for large values of lambda --which produces sparse models-- the variation is smaller, which confirms my guess. – Taha Feb 10 '13 at 6:42
• The bars are the standard deviation of the deviance, computed across the ten cross validation folds. – Matthew Drury Mar 12 '17 at 17:09

The green circle and dashed line locate the Lambda with minimal cross-validation error.

The blue circle and dashed line locate the point with minimal cross-validation error plus one standard deviation.