std.coef | R Documentation |

Standardize model coefficients by Standard Deviation or Partial Standard Deviation.

```
std.coef(x, partial.sd, ...)
partial.sd(x)
# Deprecated:
beta.weights(model)
```

`x, model` |
a fitted model object. |

`partial.sd` |
logical, if set to |

`...` |
additional arguments passed to |

Standardizing model coefficients has the same effect as centring and
scaling the input variables. “Classical” standardized coefficients
are calculated as
```
\beta^{*}_i = \beta_i\frac{s_{X_{i}}}{s_{y}}
```

, where
`\beta`

is the unstandardized coefficient,
`s_{X_{i}}`

is the standard deviation of associated dependent variable
`X_i`

and
`s_{y}`

is SD of the response variable.

If variables are intercorrelated, the standard deviation of
`X_i`

used in computing the standardized coefficients
`\beta_i^{*}`

should be
replaced by the partial standard deviation of
`X_i`

which is adjusted for
the multiple correlation of
`X_i`

with the other `X`

variables
included in the regression equation. The partial standard deviation is
calculated as
```
s_{X_{i}}^{*}=s_{X_{i}} VIF(X_i)^{-0.5} (\frac{n-1}{n-p} )^{0.5}
```

,
where `VIF` is the variance inflation factor,
`n` is the number of observations and `p`, the number of predictors in
the model. The coefficient is then transformed as
```
\beta^{*}_i = \beta_i s_{X_{i}}^{*}
```

.

A matrix with at least two columns for the standardized coefficient estimate and its standard error. Optionally, the third column holds degrees of freedom associated with the coefficients.

Kamil Bartoń. Variance inflation factors calculation is based
on function `vif`

from package car written by Henric Nilsson and John
Fox.

Cade, B.S. 2015 Model averaging and muddled multimodel inferences.
*Ecology* **96**, 2370-2382.

Afifi, A., May, S., Clark, V.A. 2011 *Practical Multivariate Analysis*,
Fifth Edition. CRC Press.

Bring, J. 1994 How to standardize regression coefficients. *The American
Statistician* **48**, 209–213.

`partial.sd`

can be used with `stdize`

.

`coef`

or `coeffs`

and `coefTable`

for
unstandardized coefficients.

```
# Fit model to original data:
fm <- lm(y ~ x1 + x2 + x3 + x4, data = GPA)
# Partial SD for the default formula: y ~ x1 + x2 + x3 + x4
psd <- partial.sd(lm(data = GPA))[-1] # remove first element for intercept
# Standardize data:
zGPA <- stdize(GPA, scale = c(NA, psd), center = TRUE)
# Note: first element of 'scale' is set to NA to ignore the first column 'y'
# Coefficients of a model fitted to standardized data:
zapsmall(coefTable(stdizeFit(fm, newdata = zGPA)))
# Standardized coefficients of a model fitted to original data:
zapsmall(std.coef(fm, partial = TRUE))
# Standardizing nonlinear models:
fam <- Gamma("inverse")
fmg <- glm(log(y) ~ x1 + x2 + x3 + x4, data = GPA, family = fam)
psdg <- partial.sd(fmg)
zGPA <- stdize(GPA, scale = c(NA, psdg[-1]), center = FALSE)
fmgz <- glm(log(y) ~ z.x1 + z.x2 + z.x3 + z.x4, zGPA, family = fam)
# Coefficients using standardized data:
coef(fmgz) # (intercept is unchanged because the variables haven't been
# centred)
# Standardized coefficients:
coef(fmg) * psdg
```

MuMIn documentation built on March 31, 2023, 8:33 p.m.

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