Standardized beta coefficients are definded as<\/p>\n
beta = b * sd_x\/sd_y<\/p>\n
where b are the coefficients from OLS linear regression, and sd_x and sd_y are standard deviations of each x variable and of y.<\/p>\n
In the case where you performe a robust linear regression, sd_x and sd_y seems not be very meanigfull anymore, because variances and hence standard deviations are not robust. The R package “robust” provides the function covRob() to compute a robust covariance estimator.<\/p>\n
I have written the following function to compute standardized beta coefficients for a robust linear regression. Setting the parameter classic=TRUE gives you the classic estimation of the beta coefficients. For very bad data, the covRob() function cannot compute the covariance due singularities. In\u00a0this case the classical estimator is returned.<\/p>\n
my.lmr.beta <- function (object, classic = FALSE) {\r\n if(class(object) != \"lmRob\")\r\n stop(\"Object must be of class 'lmRob'\")\r\n model <- object$model\r\n num <- sapply(model, is.numeric) # numeric vars only\r\n b <- object$coefficients[num][-1] # final coefficients w\/o intercept\r\n ## compute robust covariance\r\n covr <- NULL\r\n try(covr <- diag(covRob(model[num])$cov), silent = TRUE)\r\n if(is.null(covr) & classic == FALSE)\r\n warning(\"covRob() coud not be computed, instead covClassic() was applied.\")\r\n ## compute classic covariance if robust failed\r\n if(is.null(covr) | classic == TRUE)\r\n covr <- diag(covClassic(model[num])$cov)\r\n sx <- sqrt(covr[-1]) # standard deviation of x's\r\n sy <- sqrt(covr[1]) # standard deviation of y\r\n beta <- b * sx\/sy\r\n return(beta)\r\n}<\/pre>\n\u00a0UPDATE — 2014-07-23<\/p>\n<\/strong>Computing standard deviations for factors makes sense, because variance\u00a0is definded for the binomial distribution. \u00a0So I have removed the num variable.<\/p>\n
my.lmr.beta <- function (object, classic = FALSE) {\r\n if(class(object) != \"lmRob\")\r\n stop(\"Object must be of class 'lmRob'\")\r\n model <- object$model\r\n #num <- sapply(model, is.numeric) # numeric vars only\r\n b <- object$coefficients[-1] # final coefficients w\/o intercept\r\n ## compute robust covariance\r\n covr <- NULL\r\n try(covr <- diag(covRob(model)$cov), silent = TRUE)\r\n if(is.null(covr) & classic == FALSE)\r\n warning(\"covRob() coud not be computed, instead covClassic() was applied.\")\r\n ## compute classic covariance if robust failed\r\n if(is.null(covr) | classic == TRUE)\r\n covr <- diag(covClassic(sapply(model, as.numeric))$cov)\r\n sx <- sqrt(covr[-1]) # standard deviation of x's\r\n sy <- sqrt(covr[1]) # standard deviation of y\r\n beta <- b * sx\/sy\r\n return(beta)\r\n}<\/pre>\n <\/p>\n","protected":false},"excerpt":{"rendered":"
Standardized beta coefficients are definded as beta = b * sd_x\/sd_y where b are the coefficients from OLS linear regression, and sd_x and sd_y are standard deviations of each x variable and of y. In the case where you performe a robust linear regression, sd_x and sd_y seems not be very meanigfull anymore, because variances … Continue reading Robust Standardized Beta Coefficients<\/span>