Instead, we propose placing an absolute value penalty on parameter estimates, whereby unimportant variables have their estimated association shrunk to zero.
The Lasso imposes a penalty on the parameters during likelihood optimization, essentially constraining the magnitude of the sum of the absolute values of the parameter values to be small [ 20].
The LASSO row corresponds to a classical linear least squares regression:, realized on each dimension (gene) subject to an penalty on the parameters.
Although larger parameter estimates are always more heavily penalized, methods that apply larger relative penalties on small parameter estimates and relatively lower penalties to larger estimates seem to perform better and more accurately estimate the effect size of the selected SNPs.
In order to avoid a rapid increasing behavior on penalty parameters, the constants should be set to values close to 1. .
This adjustment places a heavier penalty on the number of parameters when the number of observations is not much larger than the number of parameters; thus AICc tends to choose a simpler model than AIC.
The second term, kln (n), serves as a penalty on the number of parameters used in the model to avoid overfitting.
In place of the Akaike information criterion (AIC) we used the corrected AIC (AICc), which imposes a penalty on the number of parameters for finite or sparse samples.
It is more proper to speak of goodness of fit, a measure which generally includes some sort of penalty on the number of parameters used as well as the sum of the squared error.
Comparisons of the estimated models were done taking advantage of the Akaike information criterion (AIC), which combines the goodness of fit of a model and a penalty on the number of parameters in a single score.
