# Function for Standardizing Regression Predictors by Centering and Dividing by 2 sd's Numeric variables that take on more than two values are each rescaled to have a mean of 0 and a sd of 0.5; Binary variables are rescaled to have a mean of 0 and a difference of 1 between their two categories; Non-numeric variables that take on more than two values are unchanged; Variables that take on only one value are unchanged ```r ## S4 method for signature 'lm' standardize(object, unchanged = NULL, standardize.y = FALSE, binary.inputs = "center") ## S4 method for signature 'glm' standardize(object, unchanged = NULL, standardize.y = FALSE, binary.inputs = "center") ## S4 method for signature 'merMod' standardize(object, unchanged = NULL, standardize.y = FALSE, binary.inputs = "center") ## S4 method for signature 'polr' standardize(object, unchanged = NULL, standardize.y = FALSE, binary.inputs = "center") ``` ## Arguments - `object`: an object of class `lm` or `glm` - `unchanged`: vector of names of parameters to leave unstandardized - `standardize.y`: if TRUE, the outcome variable is standardized also - `binary.inputs`: options for standardizing binary variables ## Details "0/1" (rescale so that the lower value is 0 and the upper is 1) "-0.5/0.5" (rescale so that the lower value is -0.5 and upper is 0.5) "center" (rescale so that the mean of the data is 0 and the difference between the two categories is 1) "full" (rescale by subtracting the mean and dividing by 2 sd's) "leave.alone" (do nothing) ## References Andrew Gelman. (2008). Scaling regression inputs by dividing by two standard deviations. **Statistics in Medicine** 27: 2865--2873. [http://www.stat.columbia.edu/~gelman/research/published/standardizing7.pdf](http://www.stat.columbia.edu/~gelman/research/published/standardizing7.pdf) ## Author(s) Andrew Gelman gelman@stat.columbia.edu Yu-Sung Su suyusung@tsinghua.edu.cn ## See Also `rescale` ## Examples ```r # Set up the fake data n <- 100 x <- rnorm (n, 2, 1) x1 <- rnorm (n) x1 <- (x1-mean(x1))/(2*sd(x1)) # standardization x2 <- rbinom (n, 1, .5) b0 <- 1 b1 <- 1.5 b2 <- 2 y <- rbinom (n, 1, invlogit(b0+b1*x1+b2*x2)) y2 <- sample(1:5, n, replace=TRUE) M1 <- glm (y ~ x, family=binomial(link="logit")) display(M1) M1.1 <- glm (y ~ rescale(x), family=binomial(link="logit")) display(M1.1) M1.2 <- standardize(M1) display(M1.2) # M1.1 & M1.2 should be the same M2 <- polr(ordered(y2) ~ x) display(M2) M2.1 <- polr(ordered(y2) ~ rescale(x)) display(M2.1) M2.2 <- standardize(M2.1) display(M2.2) # M2.1 & M2.2 should be the same ```

standardize function