Description Usage Arguments Details Author(s) References See Also Examples

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

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")
``` |

`object` |
an object of class |

`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 |

"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)

Andrew Gelman gelman@stat.columbia.edu Yu-Sung Su suyusung@tsinghua.edu.cn

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

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
``` |

```
Loading required package: MASS
Loading required package: Matrix
Loading required package: lme4
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
```

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