Mono-zygotic twins reared apart: raw IQ data
Init
options(digits = 2)
library(pacman)
p_load(kirkegaard, readxl, rms)
theme_set(theme_bw())Data
Data are from Jensen, A. R. (1970). IQ’s of identical twins reared apart. Behavior Genetics, l, 133-148.
#read data
jensen = read_excel("data/Jensen 1970.xlsx")
#show data
jensenResults
#overall
GG_scatter(jensen, "A", "B", color = "Source")
ggplot(jensen, aes(A, B)) +
geom_point() +
geom_smooth(method = "lm") +
facet_wrap("Source")
#color by country
GG_scatter(jensen, "A", "B", color = "Country")
ggplot(jensen, aes(A, B)) +
geom_point() +
geom_smooth(method = "lm") +
facet_wrap("Country")
#differences
jensen %<>% mutate(
delta = A - B,
abs_delta = abs(delta)
)
#distributions of deltas
GG_denhist(jensen, "delta", "Source", vline = F)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
GG_denhist(jensen, "abs_delta", "Source", vline = F)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#numerics
#range restriction adjust
jensen %>%
group_by(Source) %>%
summarise(
n = n(),
r = wtd.cors(A, B),
mean_A = mean(A),
mean_B = mean(B),
mean_mean = mean(mean_A, mean_B),
sd_A = sd(A),
sd_B = sd(B),
sd_mean = mean(sd_A, sd_B),
r_cor = rangeCorrection(r, sdu = 15, sdr = sd_mean, case=2)
)#models
ols(A ~ B, data = jensen)## Linear Regression Model
##
## ols(formula = A ~ B, data = jensen)
##
## Model Likelihood Discrimination
## Ratio Test Indexes
## Obs 122 LR chi2 139.49 R2 0.681
## sigma7.7065 d.f. 1 R2 adj 0.679
## d.f. 120 Pr(> chi2) 0.0000 g 12.824
##
## Residuals
##
## Min 1Q Median 3Q Max
## -18.7819 -4.9573 -0.4713 5.2658 22.8402
##
##
## Coef S.E. t Pr(>|t|)
## Intercept 23.5359 4.6290 5.08 <0.0001
## B 0.7568 0.0473 16.01 <0.0001
## ols(A ~ B + Source, data = jensen)## Linear Regression Model
##
## ols(formula = A ~ B + Source, data = jensen)
##
## Model Likelihood Discrimination
## Ratio Test Indexes
## Obs 122 LR chi2 141.66 R2 0.687
## sigma7.7356 d.f. 4 R2 adj 0.676
## d.f. 117 Pr(> chi2) 0.0000 g 12.873
##
## Residuals
##
## Min 1Q Median 3Q Max
## -17.4786 -5.2505 -0.4846 4.7495 23.0357
##
##
## Coef S.E. t Pr(>|t|)
## Intercept 25.5801 4.9175 5.20 <0.0001
## B 0.7383 0.0491 15.03 <0.0001
## Source=Juel-Nielsen 2.4426 2.5123 0.97 0.3329
## Source=Newman -0.5370 2.0709 -0.26 0.7959
## Source=Shields -1.3116 1.6605 -0.79 0.4312
## ols(A ~ B * Source, data = jensen)## Linear Regression Model
##
## ols(formula = A ~ B * Source, data = jensen)
##
## Model Likelihood Discrimination
## Ratio Test Indexes
## Obs 122 LR chi2 147.22 R2 0.701
## sigma7.6600 d.f. 7 R2 adj 0.682
## d.f. 114 Pr(> chi2) 0.0000 g 12.990
##
## Residuals
##
## Min 1Q Median 3Q Max
## -16.4311 -5.0639 -0.3369 5.0465 22.5941
##
##
## Coef S.E. t Pr(>|t|)
## Intercept 15.1999 6.8990 2.20 0.0296
## B 0.8445 0.0698 12.11 <0.0001
## Source=Juel-Nielsen 40.4130 22.8897 1.77 0.0801
## Source=Newman 21.3130 14.3194 1.49 0.1394
## Source=Shields 14.9619 10.6723 1.40 0.1637
## B * Source=Juel-Nielsen -0.3647 0.2150 -1.70 0.0926
## B * Source=Newman -0.2261 0.1474 -1.53 0.1279
## B * Source=Shields -0.1696 0.1111 -1.53 0.1298
## ols(A ~ B + Country, data = jensen)## Linear Regression Model
##
## ols(formula = A ~ B + Country, data = jensen)
##
## Model Likelihood Discrimination
## Ratio Test Indexes
## Obs 122 LR chi2 141.01 R2 0.685
## sigma7.7232 d.f. 3 R2 adj 0.677
## d.f. 118 Pr(> chi2) 0.0000 g 12.865
##
## Residuals
##
## Min 1Q Median 3Q Max
## -18.3194 -5.1164 -0.4981 4.7645 23.0557
##
##
## Coef S.E. t Pr(>|t|)
## Intercept 27.4455 5.6437 4.86 <0.0001
## B 0.7437 0.0486 15.31 <0.0001
## Country=United Kingdom -2.9309 2.4312 -1.21 0.2304
## Country=United States -2.9197 2.8981 -1.01 0.3158
## ols(A ~ B * Country, data = jensen)## Linear Regression Model
##
## ols(formula = A ~ B * Country, data = jensen)
##
## Model Likelihood Discrimination
## Ratio Test Indexes
## Obs 122 LR chi2 144.27 R2 0.693
## sigma7.6862 d.f. 5 R2 adj 0.680
## d.f. 116 Pr(> chi2) 0.0000 g 12.969
##
## Residuals
##
## Min 1Q Median 3Q Max
## -18.8849 -5.0639 -0.4331 4.4666 22.5941
##
##
## Coef S.E. t Pr(>|t|)
## Intercept 55.6129 21.8999 2.54 0.0124
## B 0.4798 0.2041 2.35 0.0204
## Country=United Kingdom -34.9040 22.5129 -1.55 0.1238
## Country=United States -19.1000 25.2613 -0.76 0.4511
## B * Country=United Kingdom 0.3036 0.2111 1.44 0.1530
## B * Country=United States 0.1386 0.2421 0.57 0.5682
## #LR test of additional predictors
lrtest(ols(A ~ B, data = jensen),
ols(A ~ B * Source, data = jensen))##
## Model 1: A ~ B
## Model 2: A ~ B * Source
##
## L.R. Chisq d.f. P
## 7.73 6.00 0.26lrtest(ols(A ~ B, data = jensen),
ols(A ~ B * Country, data = jensen))##
## Model 1: A ~ B
## Model 2: A ~ B * Country
##
## L.R. Chisq d.f. P
## 4.78 4.00 0.31