standardize: Function for Standardizing Regression Predictors by Centering... In arm: Data Analysis Using Regression and Multilevel/Hierarchical Models

Description

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

Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## 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)

Author(s)

Andrew Gelman [email protected] Yu-Sung Su [email protected]

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

`rescale`

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ``` # 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(M1.1) 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 ```

Example output

```Loading required package: MASS

arm (Version 1.9-3, built: 2016-11-21)

Working directory is /work/tmp

glm(formula = y ~ x, family = binomial(link = "logit"))
coef.est coef.se
(Intercept) 1.53     0.68
x           0.29     0.33
---
n = 100, k = 2
residual deviance = 68.5, null deviance = 69.3 (difference = 0.8)
glm(formula = y ~ rescale(x), family = binomial(link = "logit"))
coef.est coef.se
(Intercept) 2.12     0.33
rescale(x)  0.57     0.66
---
n = 100, k = 2
residual deviance = 68.5, null deviance = 69.3 (difference = 0.8)
glm(formula = y ~ rescale(z.x), family = binomial(link = "logit"))
coef.est coef.se
(Intercept)  2.12     0.33
rescale(z.x) 0.57     0.66
---
n = 100, k = 2
residual deviance = 68.5, null deviance = 69.3 (difference = 0.8)

Re-fitting to get Hessian

polr(formula = ordered(y2) ~ x)
coef.est coef.se
x    0.12     0.18
1|2 -1.35     0.45
2|3 -0.43     0.42
3|4  0.60     0.42
4|5  1.45     0.45
---
n = 100, k = 5 (including 4 intercepts)
residual deviance = 318.7, null deviance is not computed by polr

Re-fitting to get Hessian

polr(formula = ordered(y2) ~ rescale(x))
coef.est coef.se
rescale(x)  0.23     0.36
1|2        -1.59     0.27
2|3        -0.67     0.21
3|4         0.36     0.20
4|5         1.21     0.24
---
n = 100, k = 5 (including 4 intercepts)
residual deviance = 318.7, null deviance is not computed by polr

Re-fitting to get Hessian

polr(formula = ordered(y2) ~ rescale(z.x))
coef.est coef.se
rescale(z.x)  0.23     0.36
1|2          -1.59     0.27
2|3          -0.67     0.21
3|4           0.36     0.20
4|5           1.21     0.24
---
n = 100, k = 5 (including 4 intercepts)
residual deviance = 318.7, null deviance is not computed by polr
```

arm documentation built on May 31, 2017, 3:34 a.m.