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Instead of using ridge regression with a fixed penalization of your coefficients it would be better to use iterated adaptive ridge regression though, as the latter approximates L0 penalized regression … regression approaches. …

The fastest option (faster than the other solutions posted here) is to observe that nnls can be reformulated as a quadratic programming problem, and that when written as a quadratic programming proble …

There is also polr in MASS that can fit the proportional odds cumulative logit model, which I like because you can show the fitted model easily using the effects package (for lrm and clm this is not t …

sums of squares of the perpendicular distance between each point and the regression line, sometimes this is referred to as Type II regression, orthogonal regression or standardized principal component … regression). …

So given that the coefficients of a ridge regression with a squared L2 norm penalty corresponds to the maximum a posteriori (MAP) estimate of a Bayesian regression with Gaussian priors on the coefficients … and LASSO regression coefficients with L1 norm penalty to the MAP estimate of a Bayesian regression with Laplace priors on the coefficients, is there any known prior distributions in Bayesian regression …

: because the coefficients will be highly biased, which is improved in relaxed LASSO, MCP and SCAD penalized regression, and resolved completely in L0 penalized regression (which has a full oracle property … The latter is in fact an option provided by all major regularized regression frameworks (e.g. glmnet, ncvreg, ordinis). Hope this helps? …

I used a binomial GLM with a log(exposure) offset in this article. I wanted to compare the proportion of stingless bee colonies that switched from building in a parallel fashion to a helicoidal fashio …

Stable computation of maximum likelihood estimates in identity link Poisson regression. Journal of Computational and Graphical Statistics 19(3): 666--683. …

I would just like to add that another way to take into account prior knowledge is to use either adaptive ridge regression or adaptive LASSO regression, where the lambdas with which you penalize your variables … In Bayesian terms, adaptive LASSO regression corresponds to assuming a Laplacian prior (exponential if nonnegativity constraints are imposed), whereas adaptive ridge regression corresponds to assuming …

L0-pseudonorm penalized least squares regression (aka best subset regression) solves $\widehat{\beta}(\lambda)$ as $$\min_\beta \frac{1}{2}||y-X\beta||_2^2 +\lambda||\beta||_0.$$ where $||\beta||_0$ is … For LASSO regression, where we work with the L1-norm penalty $\lambda||\beta||_1$ I understand that (1) is given by $\lambda_1 = \max_j |X_j^Ty|$, but what would be it's value in case of L0-penalized regression …

In fact, the LASSO ($L_1$ norm penalized regression) is the tightest convex relaxation of $L_0$ pseudonorm penalized regression / best subset selection and so is uniquely defined (bridge regression, i.e … That being said, there are also efficient computational methods now to approximate best subset selection / $L_0$ penalized regression in a very stable way. …

The other advantage of L0-penalized regression over ridge regression or LASSO regression is that it gives you unbiased estimates, so you can get rid of the bias-variance tradeoff that plagues most penalized … regression approaches. …

What about using z <- summary(test)$coefficients/summary(test)$standard.errors # 2-tailed Wald z tests to test significance of coefficients p <- (1 - pnorm(abs(z), 0, 1)) * 2 p Basically, this woul …

If you would be OK using R I think you could also use bbmle's mle2 function to optimize the least squares likelihood function and calculate 95% confidence intervals on the nonnegative nnls coefficient …

I would like to do a Shapiro Wilk's W test and Kolmogorov-Smirnov test on the residuals of a linear model to check for normality. I was just wondering what residuals should be used for this - the raw …