Homework example
Hank Lee
2020-09-14
Introduction
Ten subjects were played tones at each of 5 loudnesses, in random order. Subjects were asked to draw a line on paper whose length matched the loudness of the tone. Each subject repeated each loudness 3 times, for a total of 30 trials per subject. Here is the mean of the 3 log-lengths for each loudness, the sd of the three log-lengths, and the number of replications, which is always 3.
A data frame with 50 observations on the following 5 variables.
subject
a factor with unique values for each subject
loudness
either 50, 60, 70, 80 or 90 db. Decibels are a logrithmic scale
y
a numeric vector giving the mean of the log-lengths of three lines drawn.
sd
a numeric vector, giving the sd of the three log lengths
n
a numeric vector, equal to the constant value 3
Data management
library(tidyverse)
library(haven)
fL <- "https://stats.idre.ucla.edu/stat/examples/imm/imm10.dta"
dta <- read_dta(fL)
glimpse(dta)Rows: 260
Columns: 19
$ schid <dbl> 7472, 7472, 7472, 7472, 7472, 7472, 7472, 7472, 7472, 7472...
$ stuid <dbl> 3, 8, 13, 17, 27, 28, 30, 36, 37, 42, 52, 53, 61, 64, 72, ...
$ ses <dbl> -0.13, -0.39, -0.80, -0.72, -0.74, -0.58, -0.83, -0.51, -0...
$ meanses <dbl> -0.48261, -0.48261, -0.48261, -0.48261, -0.48261, -0.48261...
$ homework <dbl> 1, 0, 0, 1, 2, 1, 5, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1...
$ white <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1...
$ parented <dbl> 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 1, 2, 3, 3, 1, 3, 3...
$ public <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1...
$ ratio <dbl> 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19...
$ percmin <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0...
$ math <dbl> 48, 48, 53, 42, 43, 57, 33, 64, 36, 56, 48, 48, 44, 35, 50...
$ sex <dbl> 2, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1...
$ race <dbl> 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4...
$ sctype <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1...
$ cstr <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2...
$ scsize <dbl> 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3...
$ urban <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2...
$ region <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2...
$ schnum <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1...library(tidyverse)
library(lme4)dta$schid <- factor(dta$schid)OLS regression lines over 10 subjects
coef(m0 <- nlme::lmList(math ~ homework | schid, data=dta)) (Intercept) homework
7472 50.684 -3.5538
7829 49.012 -2.9201
7930 38.750 7.9091
24725 34.394 5.5927
25456 53.939 -4.7184
25642 49.259 -2.4861
62821 59.210 1.0946
68448 36.055 6.4963
68493 38.520 5.8600
72292 37.714 6.3351Visualization
ggplot(data=dta, aes(homework, math, color=schid)) +
geom_point(alpha=0.5) +
stat_smooth(aes(group=1), method="lm", formula=y~x) +
stat_smooth(method="lm", formula=y ~ x, se=F) +
labs(x="Homework (hours per week)",
y="Math score") +
guides(color=guide_legend(ncol=2))+
theme_minimal() +
theme(legend.position=c(.9,.3))