To install the standardize package, call:
install.packages("standardize")The standardize package provides tools for controlling continuous variable scaling and factor contrasts. The goal of these standardizations is to keep the regression parameters on similar scales, and to ensure that the intercept (which is the predicted value of an observation when all other coefficients are multiplied by 0) represents the corrected mean (i.e. the predicted value for an observation which is average in every way, holding covariates at their mean values and averaging over group differences in factors). When the predictors are all on a similar scale, there are computational benefits for both frequentist and Bayesian approaches in mixed effects regressions, reasonable Bayesian priors are easier to specify, and regression output is easier to interpret. Take, for example, the ptk dataset included in the package (for which we will create a new ordered factor preheight):
library(standardize)
#>
#> ***********************************************************
#> Loading standardize package version 0.2.2
#> Call standardize.news() to see new features/changes
#> ***********************************************************
ptk$preheight <- "Mid"
ptk$preheight[ptk$prevowel == "a"] <- "Low"
ptk$preheight[ptk$prevowel %in% c("i", "u")] <- "High"
ptk$preheight <- factor(ptk$preheight, ordered = TRUE, levels = c("Low",
"Mid", "High"))
summary(ptk)
#> cdur vdur place stress prevowel
#> Min. : 61.0 Min. : 0.00 Bilabial:228 Post-Tonic:250 a:217
#> 1st Qu.:117.0 1st Qu.: 49.00 Dental :275 Tonic :252 e:169
#> Median :133.0 Median : 62.00 Velar :248 Unstressed:249 i:146
#> Mean :137.5 Mean : 60.69 o:151
#> 3rd Qu.:155.0 3rd Qu.: 77.00 u: 68
#> Max. :281.0 Max. :190.00
#>
#> posvowel wordpos wordfreq speechrate sex
#> a:212 Initial:322 Min. : 1 Min. : 2.000 Female:384
#> e:144 Medial :429 1st Qu.: 1104 1st Qu.: 5.000 Male :367
#> i: 86 Median : 4899 Median : 6.000
#> o:255 Mean : 18840 Mean : 5.812
#> u: 54 3rd Qu.: 26610 3rd Qu.: 7.000
#> Max. :158168 Max. :10.000
#>
#> speaker preheight
#> s02 : 45 Low :217
#> s03 : 45 Mid :320
#> s04 : 45 High:214
#> s07 : 45
#> s11 : 45
#> s16 : 44
#> (Other):482Suppose we want to fit a linear mixed effects regression with total consonant duration cdur as the response, place, stress, preheight, the natural log of wordfreq, and speaker-relative speechrate as fixed effects, and random intercepts for speaker. The variables for this regression can be easily placed into a standardized space with the standardize function:
sobj <- standardize(cdur ~ place + stress + preheight + log(wordfreq) +
scale_by(speechrate ~ speaker) + (1 | speaker), ptk)
sobj
#>
#> Call:
#> standardize(formula = cdur ~ place + stress + preheight + log(wordfreq) +
#> scale_by(speechrate ~ speaker) + (1 | speaker), data = ptk)
#>
#> Family: gaussian
#> Link function: identity
#>
#> Standardized Formula:
#> cdur ~ place + stress + preheight + log_wordfreq + speechrate_scaled_by_speaker +
#> (1 | speaker)
#>
#> Variables:
#> Variable Standardized Name Class
#> cdur cdur response.numeric
#> place place factor
#> stress stress factor
#> preheight preheight ordered
#> log(wordfreq) log_wordfreq numeric
#> scale_by(speechrate ~ speaker) speechrate_scaled_by_speaker scaledby
#> speaker speaker group
#>
#> Response has mean 0 and standard deviation 1.
#>
#> Continuous variables have mean 0 and standard deviation 1
#> (within-factor-level if scale_by was used)
#> Unordered factors have sum contrasts with deviation 1
#> Ordered factors have orthogonal polynomial contrasts whose
#> columns have standard deviation 1
#> Grouping factors are coded as unordered factors with default contrasts
names(sobj)
#> [1] "call" "scale" "formula" "family" "data" "offset"
#> [7] "pred" "variables" "contrasts" "groups"
head(sobj$data)
#> cdur place stress preheight log_wordfreq
#> 1 0.58032620 Velar Unstressed Low -1.64753617
#> 2 0.21456174 Velar Post-Tonic High -1.64753617
#> 3 -0.11795140 Dental Unstressed High -0.05570344
#> 4 0.01505386 Dental Post-Tonic High -1.90076049
#> 5 0.91283934 Velar Tonic Mid -0.19203879
#> 6 1.51136300 Dental Post-Tonic High -0.22152148
#> speechrate_scaled_by_speaker speaker
#> 1 -0.4984662 s01
#> 2 1.3452937 s01
#> 3 -0.4984662 s01
#> 4 0.6454974 s01
#> 5 2.2671736 s01
#> 6 -2.3422261 s01
mean(sobj$data$cdur)
#> [1] -1.539605e-16
sd(sobj$data$cdur)
#> [1] 1
mean(sobj$data$log_wordfreq)
#> [1] 1.550764e-16
sd(sobj$data$log_wordfreq)
#> [1] 1
all.equal(scale(log(ptk$wordfreq))[, 1], sobj$data$log_wordfreq[, 1])
#> [1] TRUE
with(sobj$data, tapply(speechrate_scaled_by_speaker, speaker, mean))
#> s01 s02 s03 s04 s05
#> -2.960268e-16 3.165268e-18 -3.119346e-16 1.004790e-16 2.183358e-16
#> s06 s07 s08 s09 s10
#> -7.174906e-17 -1.953684e-16 -2.200950e-16 1.468327e-16 -1.266348e-16
#> s11 s12 s13 s14 s15
#> -2.923792e-16 3.850162e-16 1.980309e-16 6.325185e-17 1.427623e-16
#> s16 s17 s18
#> -2.220446e-16 1.582818e-16 -2.505491e-16
with(sobj$data, tapply(speechrate_scaled_by_speaker, speaker, sd))
#> s01 s02 s03 s04 s05 s06 s07 s08 s09 s10 s11 s12 s13 s14 s15 s16 s17 s18
#> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
sobj$contrasts
#> $place
#> Bilabial Dental
#> Bilabial 1 0
#> Dental 0 1
#> Velar -1 -1
#>
#> $stress
#> Post-Tonic Tonic
#> Post-Tonic 1 0
#> Tonic 0 1
#> Unstressed -1 -1
#>
#> $preheight
#> .L .Q
#> Low -1.00000e+00 0.5773503
#> Mid -3.32076e-17 -1.1547005
#> High 1.00000e+00 0.5773503
sobj$groups
#> $speaker
#> [1] "s01" "s02" "s03" "s04" "s05" "s06" "s07" "s08" "s09" "s10" "s11" "s12"
#> [13] "s13" "s14" "s15" "s16" "s17" "s18"The default settings for standardize have placed all the continuous variables on unit scale, set (named) sum contrasts for all unordered factors, and orthogonal polynomial contrasts with column standard deviations of 1 for all ordered factors. In the case of speechrate, the call to scale_by ensured that rather than simply placing speechrate on unit scale, it was placed on unit scale for each speaker, so that the resulting variable represents speaker-relative speech rate. We can then simply use the formula and data elements of the object returned by standardize to fit the mixed effects regression in this standardized space:
library(lme4)
#> Loading required package: Matrix
#> Warning: package 'Matrix' was built under R version 3.6.3
mod <- lmer(sobj$formula, sobj$data)
summary(mod)
#> Linear mixed model fit by REML ['lmerMod']
#> Formula:
#> cdur ~ place + stress + preheight + log_wordfreq + speechrate_scaled_by_speaker +
#> (1 | speaker)
#> Data: sobj$data
#>
#> REML criterion at convergence: 2018
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -2.5479 -0.6919 -0.1014 0.5883 4.2981
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> speaker (Intercept) 0.09375 0.3062
#> Residual 0.79081 0.8893
#> Number of obs: 751, groups: speaker, 18
#>
#> Fixed effects:
#> Estimate Std. Error t value
#> (Intercept) 0.015759 0.079462 0.198
#> placeBilabial 0.008255 0.047766 0.173
#> placeDental -0.011703 0.045913 -0.255
#> stressPost-Tonic -0.062456 0.048407 -1.290
#> stressTonic 0.212176 0.047974 4.423
#> preheight.L 0.017645 0.046657 0.378
#> preheight.Q 0.059551 0.039241 1.518
#> log_wordfreq -0.037784 0.033815 -1.117
#> speechrate_scaled_by_speaker -0.306867 0.033216 -9.239
#>
#> Correlation of Fixed Effects:
#> (Intr) plcBlb plcDnt strP-T strssT prhg.L prhg.Q lg_wrd
#> placeBilabl 0.024
#> placeDental -0.039 -0.500
#> strssPst-Tn 0.004 0.053 -0.051
#> stressTonic -0.006 0.003 -0.003 -0.524
#> preheight.L 0.009 0.075 -0.106 -0.272 0.276
#> preheight.Q 0.083 -0.041 -0.127 0.029 -0.059 0.023
#> log_wordfrq 0.005 -0.092 0.062 -0.131 -0.029 0.106 0.093
#> spchrt_sc__ 0.007 0.015 -0.043 0.058 0.046 0.061 0.073 0.013The scaling of the predictors can be controlled through the scale argument to standardize. For example:
sobj <- standardize(cdur ~ place + stress + preheight + log(wordfreq) +
scale_by(speechrate ~ speaker) + (1 | speaker), ptk, scale = 0.5)
sobj
#>
#> Call:
#> standardize(formula = cdur ~ place + stress + preheight + log(wordfreq) +
#> scale_by(speechrate ~ speaker) + (1 | speaker), data = ptk,
#> scale = 0.5)
#>
#> Family: gaussian
#> Link function: identity
#>
#> Standardized Formula:
#> cdur ~ place + stress + preheight + log_wordfreq + speechrate_scaled_by_speaker +
#> (1 | speaker)
#>
#> Variables:
#> Variable Standardized Name Class
#> cdur cdur response.numeric
#> place place factor
#> stress stress factor
#> preheight preheight ordered
#> log(wordfreq) log_wordfreq numeric
#> scale_by(speechrate ~ speaker) speechrate_scaled_by_speaker scaledby
#> speaker speaker group
#>
#> Response has mean 0 and standard deviation 1.
#>
#> Continuous variables have mean 0 and standard deviation 0.5
#> (within-factor-level if scale_by was used)
#> Unordered factors have sum contrasts with deviation 0.5
#> Ordered factors have orthogonal polynomial contrasts whose
#> columns have standard deviation 0.5
#> Grouping factors are coded as unordered factors with default contrasts
names(sobj)
#> [1] "call" "scale" "formula" "family" "data" "offset"
#> [7] "pred" "variables" "contrasts" "groups"
head(sobj$data)
#> cdur place stress preheight log_wordfreq
#> 1 0.58032620 Velar Unstressed Low -0.82376808
#> 2 0.21456174 Velar Post-Tonic High -0.82376808
#> 3 -0.11795140 Dental Unstressed High -0.02785172
#> 4 0.01505386 Dental Post-Tonic High -0.95038025
#> 5 0.91283934 Velar Tonic Mid -0.09601939
#> 6 1.51136300 Dental Post-Tonic High -0.11076074
#> speechrate_scaled_by_speaker speaker
#> 1 -0.2492331 s01
#> 2 0.6726468 s01
#> 3 -0.2492331 s01
#> 4 0.3227487 s01
#> 5 1.1335868 s01
#> 6 -1.1711131 s01
mean(sobj$data$cdur)
#> [1] -1.539605e-16
sd(sobj$data$cdur)
#> [1] 1
mean(sobj$data$log_wordfreq)
#> [1] 7.753821e-17
sd(sobj$data$log_wordfreq)
#> [1] 0.5
all.equal(0.5 * scale(log(ptk$wordfreq))[, 1], sobj$data$log_wordfreq[, 1])
#> [1] TRUE
with(sobj$data, tapply(speechrate_scaled_by_speaker, speaker, mean))
#> s01 s02 s03 s04 s05
#> -1.480134e-16 1.582634e-18 -1.559673e-16 5.023952e-17 1.091679e-16
#> s06 s07 s08 s09 s10
#> -3.587453e-17 -9.768421e-17 -1.100475e-16 7.341635e-17 -6.331741e-17
#> s11 s12 s13 s14 s15
#> -1.461896e-16 1.925081e-16 9.901544e-17 3.162593e-17 7.138116e-17
#> s16 s17 s18
#> -1.110223e-16 7.914090e-17 -1.252746e-16
with(sobj$data, tapply(speechrate_scaled_by_speaker, speaker, sd))
#> s01 s02 s03 s04 s05 s06 s07 s08 s09 s10 s11 s12 s13 s14 s15 s16 s17 s18
#> 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
sobj$contrasts
#> $place
#> Bilabial Dental
#> Bilabial 0.5 0.0
#> Dental 0.0 0.5
#> Velar -0.5 -0.5
#>
#> $stress
#> Post-Tonic Tonic
#> Post-Tonic 0.5 0.0
#> Tonic 0.0 0.5
#> Unstressed -0.5 -0.5
#>
#> $preheight
#> .L .Q
#> Low -5.00000e-01 0.2886751
#> Mid -1.66038e-17 -0.5773503
#> High 5.00000e-01 0.2886751
sobj$groups
#> $speaker
#> [1] "s01" "s02" "s03" "s04" "s05" "s06" "s07" "s08" "s09" "s10" "s11" "s12"
#> [13] "s13" "s14" "s15" "s16" "s17" "s18"The standardize function works by making use of the function scale from base R, as well as the standardize functions scale_by, named_contr_sum, and scaled_contr_poly. For more details, install the package and see the vignette “Using the standardize Package”.