Generic function to preduce predictive margins¶
Description¶
Generic function to preduce predictive margins
Usage¶
predmarg(
obj,
settings,
data,
subset,
groups = NULL,
setup = NULL,
cifunc = cinorm,
level = 0.95,
parallel = TRUE,
mc.cores = if (.Platform$OS.type == "windows") 1L else max.cores,
...
)
Arguments¶
obj
-
a model object, e.g. returned by
lm
,glm
, etc. settings
-
an optional data frame of settings for independent variables.
data
-
an optional data frame for which the predictive margins are computed. If ommited, an attempt is made to obtain the data from the model object.
subset
-
an optional logical vector that defines a subset for which a predictive margin is computed
groups
-
a variable that defines groups for which predictive margines are computed. This variable has to have the same number of observations as the data to which the model was fitted.
setup
-
an optional expression that is evaluated for each setting, i.e. individually for each row of the settings data frame. Can be used to modify independent variables.
cifunc
-
a function to compute prediction intervals.
level
-
level of confidence intervals of predictions.
parallel
-
logical value that determines whether predictions for individual settings are computed in parallel. (Does not yet work on windows.)
mc.cores
-
number of CPU cores used for parallel processing.
...
-
optional vectors of values of independent variabls. These further arguments, if present, are used to create a data frame of settings, using
expand.grid
.
Value¶
a data frame with the following variables:
- pred
-
the mean prediction for the setting of the independent variables
- var.pred
-
the (estimated) variance of the mean prediction
- se.pred
-
the standard error of prediction, i.e. the square root of the variance of the mean prediction
- lower
-
lower prediction interval computed with
qfunc
- upper
-
upper prediction interval computed with
qfunc
- …
-
the independent variables for which values are set to create the predictions are also included in the resulting data frame.
Details¶
The generic function predmarg
computes predictive margins for various settings of the
independent variables. It is also possible to provide settings for independent variables
that are included in the model, but that are used in the setup
expression to
transform independent variables. See the examples below.
Examples¶
library(magrittr)
# Simple linear regression
fm <- lm(weight ~ poly(height, 2), data = women)
pm <-predmarg(fm,
height=seq(from=58,to=72,
length=10))
Using 12 cores ...
str(pm)
'data.frame': 10 obs. of 6 variables:
$ pred : num 115 119 123 128 133 ...
$ var.pred: num 0.00983 0.00983 0.00983 0.00983 0.00983 ...
$ se.pred : num 0.0992 0.0992 0.0992 0.0992 0.0992 ...
$ lower : num 115 119 123 127 132 ...
$ upper : num 115 119 123 128 133 ...
$ height : num 58 59.6 61.1 62.7 64.2 ...
plot(pred~height,data=pm,
type="l")
with(women, points(height,weight))
with(pm, lines(height,lower,lty=2))
with(pm, lines(height,upper,lty=2))
# Logistic regression
library(carData)
Chile %<>% within({
vote2 <- factor(vote,levels=c("N","Y"))
vote2 <- as.integer(vote2=="Y")
})
glm.Chile.1 <- glm(vote2~sex+age+income+education,
data=Chile,
family=binomial)
summary(glm.Chile.1)
Call:
glm(formula = vote2 ~ sex + age + income + education, family = binomial,
data = Chile)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.6676 -1.1139 -0.7329 1.1194 1.7335
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.053e-01 1.786e-01 0.589 0.555615
sexM -5.415e-01 1.009e-01 -5.365 8.10e-08 ***
age 1.203e-02 3.594e-03 3.347 0.000817 ***
income 4.481e-06 1.342e-06 3.339 0.000840 ***
educationPS -1.125e+00 1.656e-01 -6.791 1.12e-11 ***
educationS -6.369e-01 1.207e-01 -5.276 1.32e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 2361.7 on 1703 degrees of freedom
Residual deviance: 2239.0 on 1698 degrees of freedom
(996 observations deleted due to missingness)
AIC: 2251
Number of Fisher Scoring iterations: 4
pm.Chile.1.income <- predmarg(glm.Chile.1,
income=seq(from=2500,to=200000,length=20))
Using 12 cores ...
plot(pred~income,data=pm.Chile.1.income,
type="l")
# Baseline category logit
library(mclogit)
Loading required package: Matrix
library(MASS)
mb.Chile <- mblogit(vote~statusquo,
data=Chile)
Iteration 1 - Deviance = 4528.43
Iteration 2 - Deviance = 4394.717
Iteration 3 - Deviance = 4383.817
Iteration 4 - Deviance = 4383.674
Iteration 5 - Deviance = 4383.674
converged
pm.mb.Chile <- predmarg(mb.Chile,
statusquo=seq(from=-2,to=2,length=20))
Using 12 cores ...
str(pm.mb.Chile)
'data.frame': 80 obs. of 8 variables:
$ pred : num 0.018123 0.950795 0.030231 0.000851 0.025456 ...
$ var.pred : num 3.78e-06 1.77e-05 7.00e-06 7.21e-09 7.21e-06 ...
$ se.pred : num 1.94e-03 4.20e-03 2.65e-03 8.49e-05 2.68e-03 ...
$ lower : num 0.014315 0.942554 0.025044 0.000685 0.020194 ...
$ upper : num 0.02193 0.95904 0.03542 0.00102 0.03072 ...
$ eqnum : int 1 2 3 4 1 2 3 4 1 2 ...
$ statusquo: num -2 -2 -2 -2 -1.79 ...
$ response : Factor w/ 4 levels "A","N","U","Y": 1 2 3 4 1 2 3 4 1 2 ...
library(ggplot2)
Attaching package: 'ggplot2'
The following object is masked from 'package:memisc':
syms
The following object is masked from 'package:crayon':
%+%
(ggplot(pm.mb.Chile,
aes(x=statusquo,
y=pred,
fill=response
)
) + geom_area())
(ggplot(pm.mb.Chile,
aes(x=statusquo,
y=pred,
ymin=lower,
ymax=upper
)
) + geom_line() +geom_ribbon(alpha=.25) + facet_grid(~response))
mb.hs <- mblogit(Sat~Infl+Type+Cont,weights=Freq,
data=housing)
Iteration 1 - Deviance = 3493.764
Iteration 2 - Deviance = 3470.111
Iteration 3 - Deviance = 3470.084
Iteration 4 - Deviance = 3470.084
converged
pm.mb.hs <- predmarg(mb.hs,
Infl=levels(Infl),
Type=levels(Type))
Using 12 cores ...
dodge <- position_dodge(width=.8)
(ggplot(pm.mb.hs)
+facet_wrap(~Type)
+geom_bar(
aes(fill=response,
x=Infl,
y=pred),
stat='identity',position=dodge,width=.8)
+geom_errorbar(
aes(x=Infl,
ymin=lower,
ymax=upper,group=response),
position=dodge,width=.4))
# Baseline category logit with random effects
# Some artificial data
exadata <- local({
B <- cbind(c(-.5,.3),
c(.5,-.5))
set.seed(42)
x <- rnorm(n=60)
X <- cbind(1,x)
Eta <- X %*% B
j <- rep(1:10,6)
jf <- as.factor(j)
u1 <- rnorm(n=10,sd=.8)
u2 <- rnorm(n=10,sd=.8)
Eta <- Eta + cbind(u1[j],x*u2[j])
expEta <- cbind(1,exp(Eta))
sum.expEta <- rowSums(expEta)
pi <- expEta/sum.expEta
Y <- t(apply(pi,1,rmultinom,n=1,size=300))
res <-data.frame(Y,x,j,jf)
names(res)[1:3] <- paste0("y",1:3)
res
})
# Baseline logit model with random intercepts and random slopes
mbrsl <- mblogit(cbind(y1,y2,y3)~x,data=exadata,
random = ~1+x|j)
Iteration 1 - deviance = 288.6454 - criterion = 0.2327619
Iteration 2 - deviance = 280.0621 - criterion = 0.001978202
Iteration 3 - deviance = 280.4586 - criterion = 2.825173e-05
Iteration 4 - deviance = 280.673 - criterion = 1.567796e-06
Iteration 5 - deviance = 280.7528 - criterion = 1.658424e-07
Iteration 6 - deviance = 280.7821 - criterion = 2.001306e-08
Iteration 7 - deviance = 280.793 - criterion = 2.668305e-09
converged
summary(mbrsl)
Call:
mblogit(formula = cbind(y1, y2, y3) ~ x, data = exadata, random = ~1 +
x | j)
Equation for y2 vs y1:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.10133 0.17623 -0.575 0.565
x 0.33688 0.06356 5.300 1.16e-07 ***
Equation for y3 vs y1:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.4734 0.0369 12.831 < 2e-16 ***
x -0.6745 0.2047 -3.295 0.000986 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Co-)Variances:
Grouping level: 1
Estimate Std.Err.
y2~1 0.304766 1.886e-02
y3~1 0.001329 0.009325 5.606e-04 2.324e-05
y2~x -0.020697 0.007922 0.034540 3.405e-03 1.240e-04 7.388e-04
y3~x 0.113854 0.011080 -0.050176 0.413338 2.435e-02 9.316e-04 5.361e-03
3.936e-02
Null Deviance: 5127
Residual Deviance: 280.8
Number of Fisher Scoring iterations: 7
Number of observations: 60
# Predictive margins for values of x
pm.mbrsl <- predmarg(mbrsl,x=seq(from=min(x),to=max(x),length=24))
Using 12 cores ...
(ggplot(pm.mbrsl,
aes(x=x,
y=pred,
fill=response
)
) + geom_area())
# Predictive margins for the random effects
pm.mbrsl.j <- predmarg(mbrsl,j=1:10)
Using 12 cores ...
(ggplot(pm.mbrsl.j,
aes(x=j,
y=pred,
fill=response
)
) + geom_bar(position="fill",stat="identity"))
pm.mbrsl.jx <- predmarg(mbrsl,
j=1:10,
x=seq(from=min(x),to=max(x),
length=24))
Using 12 cores ...
(ggplot(pm.mbrsl.jx,
aes(x=x,
y=pred,
fill=response
)
) + geom_area()
+ facet_wrap(~j))