Coding for Multi-Group Analyses
Import data and change variable names.
tbl.2 <- read_xlsx(here("data", "BEER.xlsx"))
colnames(tbl.2) <- c("bubb", 'beer', 'salt')
View data table
ks <- function(t, c) {
kable(t, caption = c, format = 'html', escape = F, digits = 3) %>%
kable_styling(full_width = F, position = 'left', fixed_thead = T)
}
ks(tbl.2[1:10,], 'Beer Data (first 10 observations)')
Beer Data (first 10 observations)
bubb
|
beer
|
salt
|
12
|
guinness
|
no
|
21
|
guinness
|
no
|
5
|
guinness
|
no
|
10
|
guinness
|
no
|
20
|
guinness
|
no
|
13
|
guinness
|
no
|
24
|
heineken
|
no
|
17
|
heineken
|
no
|
26
|
heineken
|
no
|
16
|
heineken
|
no
|
Dummy Coding
Dummy code variables
tbl.2 <- tbl.2 %>%
mutate(beer.f = factor(beer),
salt.f = factor(salt))
# rename columns for each single-column matrix in 'a' with its name in a
reCol <- function(a) {
n <- names(a)
for (i in 1:length(a)) {
colnames(a[[i]]) <- c(str_sub(n[i], end = 4L))
}
a
}
tbl.2 %>%
select_if(is.factor) %>%
map(contrasts) %>%
reCol() %>%
ks("Dummy Codes")
Dummy Codes
|
beer
|
guinness
|
0
|
heineken
|
1
|
|
|
Analyze dummy-coded data
fit.2.a <- lm(bubb ~ beer.f + salt.f +
beer.f * salt.f, tbl.2)
fit.2.a %>%
tidy() %>%
ks('Regression: Interaction of Beer and Salt')
Regression: Interaction of Beer and Salt
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
13.500
|
2.332
|
5.789
|
0.000
|
beer.fheineken
|
9.667
|
3.298
|
2.931
|
0.008
|
salt.fyes
|
7.167
|
3.298
|
2.173
|
0.042
|
beer.fheineken:salt.fyes
|
16.833
|
4.664
|
3.609
|
0.002
|
tbl.2.e <- tibble(beer.f = factor(c("guinness", "guinness",
"heineken", "heineken")),
salt.f = factor(c("no", 'yes', 'no', 'yes')))
tbl.2.b <- predict(fit.2.a, newdata = tbl.2.e) %>%
set_names(c("irish", "irish & salty",
"dutch", "dutch & salty")) %>%
enframe(name = "combo", value = 'bubbles')
tbl.2.b %>%
ks('Predicted Number of Bubbles')
Predicted Number of Bubbles
combo
|
bubbles
|
irish
|
13.500
|
irish & salty
|
20.667
|
dutch
|
23.167
|
dutch & salty
|
47.167
|
1:2 %>%
map_dbl(~ tbl.2.b$bubbles[.*2] / tbl.2.b$bubbles[.]) %>%
set_names(c('guinness','heineken')) %>%
enframe("beer", "salt multiplier") %>%
ks('Effect of Salt by Beer')
Effect of Salt by Beer
beer
|
salt multiplier
|
guinness
|
1.531
|
heineken
|
2.282
|
Contrast Coding
Contrast code variables
tbl.2 <- tbl.2 %>%
mutate_if(~ is.factor(.) && contrasts(.)[1] != -.5, list(c = ~ C(., (contr.sum(2)/(-2))))) %>%
rename_at(vars(contains('_c')),
list(~ paste(gsub('.f_c', '', .), 'c', sep = '.')))
tbl.2 %>%
select_at(vars(ends_with('.c'))) %>%
map(contrasts) %>%
reCol %>%
ks('Contrast Code')
Contrast Code
|
beer
|
guinness
|
-0.5
|
heineken
|
0.5
|
|
|
Analyze contrast-coded data
fit.2.b <- lm(bubb ~ beer.c + salt.c +
beer.c * salt.c, tbl.2)
fit.2.b %>%
tidy() %>%
ks('Regression: Interaction of Contrast-Coded Beer and Salt')
Regression: Interaction of Contrast-Coded Beer and Salt
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
26.125
|
1.166
|
22.407
|
0.000
|
beer.c1
|
18.083
|
2.332
|
7.755
|
0.000
|
salt.c1
|
15.583
|
2.332
|
6.683
|
0.000
|
beer.c1:salt.c1
|
16.833
|
4.664
|
3.609
|
0.002
|
mean(tbl.2$bubb)
## [1] 26.125
tbl.2.c <- tbl.2.e %>%
mutate_all(~ C(., (contr.sum(2)/(-2)))) %>%
rename_all(~ paste(gsub('.f', '', .), 'c', sep = '.'))
tbl.2.d <- predict(object = fit.2.b, newdata = tbl.2.c) %>%
set_names(c("irish", "irish & salty",
"dutch", "dutch & salty")) %>%
enframe(name = "combo", value = 'bubbles')
## Warning: contrasts dropped from factor beer.c
## Warning: contrasts dropped from factor salt.c
tbl.2.d %>%
ks('Predicted Number of Bubbles (Contrast Codes)')
Predicted Number of Bubbles (Contrast Codes)
combo
|
bubbles
|
irish
|
13.500
|
irish & salty
|
20.667
|
dutch
|
23.167
|
dutch & salty
|
47.167
|
1:2 %>%
map_dbl(~ tbl.2.d$bubbles[.*2] / tbl.2.d$bubbles[.]) %>%
set_names(c('guinness','heineken')) %>%
enframe("beer", "salt multiplier") %>%
ks('Effect of Salt by Beer (Contrast Codes)')
Effect of Salt by Beer (Contrast Codes)
beer
|
salt multiplier
|
guinness
|
1.531
|
heineken
|
2.282
|
Probing Interactions
Import data and change variable names
tbl.3 <- read_xlsx(here('data', 'wfint.xlsx')) %>%
rename_all(tolower)
View data
ks(tbl.3[1:10,], 'Work and Family Data (First 10 Observations)')
Work and Family Data (First 10 Observations)
anx
|
wacon
|
warel
|
wasec
|
facon
|
farel
|
fasec
|
gen
|
wicon
|
wirel
|
wisec
|
ficon
|
firel
|
fisec
|
4.50
|
4.25
|
6.25
|
3.25
|
4.50
|
6.75
|
6.75
|
1
|
7.00
|
9.25
|
6.00
|
8.00
|
10.00
|
9.50
|
2.50
|
3.25
|
3.25
|
4.25
|
6.00
|
5.25
|
5.50
|
0
|
6.75
|
5.75
|
7.75
|
8.75
|
8.00
|
7.25
|
1.50
|
5.25
|
5.50
|
6.00
|
5.50
|
6.25
|
6.50
|
0
|
7.50
|
8.25
|
9.50
|
7.50
|
9.00
|
9.75
|
3.50
|
3.00
|
4.00
|
2.00
|
5.75
|
5.25
|
5.25
|
1
|
7.25
|
6.25
|
9.00
|
7.75
|
9.50
|
10.00
|
1.75
|
5.50
|
1.75
|
3.50
|
7.00
|
1.00
|
1.00
|
0
|
7.50
|
1.25
|
4.50
|
10.00
|
1.00
|
1.00
|
1.75
|
3.75
|
5.00
|
5.50
|
5.75
|
3.25
|
2.50
|
0
|
6.75
|
6.50
|
8.75
|
9.50
|
9.75
|
9.00
|
2.75
|
4.50
|
4.50
|
4.25
|
5.00
|
6.00
|
6.25
|
0
|
7.25
|
6.75
|
9.25
|
7.25
|
9.00
|
9.25
|
4.00
|
6.75
|
2.75
|
7.00
|
4.50
|
4.75
|
5.00
|
1
|
9.75
|
4.00
|
10.00
|
6.50
|
9.00
|
9.00
|
5.25
|
3.75
|
5.50
|
4.00
|
5.00
|
5.00
|
5.00
|
1
|
8.00
|
9.00
|
9.00
|
7.25
|
9.00
|
9.25
|
2.25
|
4.75
|
4.25
|
3.00
|
5.75
|
6.00
|
5.50
|
1
|
8.25
|
7.00
|
8.75
|
6.75
|
9.25
|
8.75
|
a. Actual Predictors
Analysis of ‘actual’ predictors, i.e., actual amount of control, relationship quality, and security at work and with the family
tbl.3 %>%
names() %>%
grep('wa|fa', ., value = TRUE) %>%
map(~ paste('anx ~', .) %>% as.formula()) %>%
map_df(~ lm(., tbl.3) %>% tidy()) %>%
ks('Regression Output for Anxiety and Actual Control, Relationship Quality, and Security')
Regression Output for Anxiety and Actual Control, Relationship Quality, and Security
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
3.231
|
0.112
|
28.967
|
0
|
wacon
|
-0.109
|
0.024
|
-4.591
|
0
|
(Intercept)
|
3.817
|
0.130
|
29.416
|
0
|
warel
|
-0.219
|
0.026
|
-8.530
|
0
|
(Intercept)
|
3.362
|
0.092
|
36.612
|
0
|
wasec
|
-0.130
|
0.018
|
-7.161
|
0
|
(Intercept)
|
3.832
|
0.149
|
25.663
|
0
|
facon
|
-0.206
|
0.028
|
-7.472
|
0
|
(Intercept)
|
3.900
|
0.153
|
25.482
|
0
|
farel
|
-0.207
|
0.027
|
-7.736
|
0
|
(Intercept)
|
3.984
|
0.140
|
28.461
|
0
|
fasec
|
-0.226
|
0.025
|
-9.098
|
0
|
b. Moderation by Gender
Analysis of gender as a moderating variable of effects on anxiety. Continuing to use ‘actual’ predictors.
Significant interactions are automatically highlighted with green text.
tbl.3.b <- tbl.3 %>%
names() %>%
grep('wa|fa', ., value = TRUE) %>%
map(~ paste('anx ~', ., '+ gen +', ., ' * gen') %>% as.formula()) %>%
map_df(~ lm(., tbl.3) %>% tidy())
tbl.3.b %>%
mutate(estimate = cell_spec(round(estimate, 3), "html",
color = ifelse(grepl(':', term) &
(p.value < .05),
"green", "black"))) %>%
ks('Regression Output for Moderation by Gender')
Regression Output for Moderation by Gender
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
3.135
|
0.195
|
16.058
|
0.000
|
wacon
|
-0.111
|
0.041
|
-2.720
|
0.007
|
gen
|
0.126
|
0.238
|
0.531
|
0.596
|
wacon:gen
|
0.008
|
0.050
|
0.155
|
0.877
|
(Intercept)
|
3.553
|
0.222
|
16.016
|
0.000
|
warel
|
-0.195
|
0.045
|
-4.304
|
0.000
|
gen
|
0.469
|
0.273
|
1.716
|
0.086
|
warel:gen
|
-0.05
|
0.055
|
-0.909
|
0.364
|
(Intercept)
|
3.22
|
0.152
|
21.162
|
0.000
|
wasec
|
-0.129
|
0.031
|
-4.155
|
0.000
|
gen
|
0.256
|
0.191
|
1.344
|
0.179
|
wasec:gen
|
-0.009
|
0.038
|
-0.238
|
0.812
|
(Intercept)
|
3.284
|
0.251
|
13.083
|
0.000
|
facon
|
-0.128
|
0.047
|
-2.693
|
0.007
|
gen
|
0.902
|
0.312
|
2.894
|
0.004
|
facon:gen
|
-0.131
|
0.058
|
-2.248
|
0.025
|
(Intercept)
|
3.138
|
0.248
|
12.650
|
0.000
|
farel
|
-0.093
|
0.044
|
-2.126
|
0.034
|
gen
|
1.251
|
0.314
|
3.985
|
0.000
|
farel:gen
|
-0.188
|
0.055
|
-3.400
|
0.001
|
(Intercept)
|
3.323
|
0.233
|
14.286
|
0.000
|
fasec
|
-0.128
|
0.041
|
-3.085
|
0.002
|
gen
|
1.033
|
0.290
|
3.558
|
0.000
|
fasec:gen
|
-0.155
|
0.052
|
-2.993
|
0.003
|
Compute the intercepts and slopes
fun.3.b <- function(i, t) {
v.e <- t[["estimate"]]
v.t <- t[["term"]]
s.m <- v.e[i]
i.m <- v.e[i - 1]
s.w <- s.m + v.e[i + 2]
i.w <- i.m + v.e[i + 1]
result <- list(term = v.t[[i]],
intercept0 = i.m, slope0 = s.m,
intercept1 = i.w, slope1 = s.w)
result
}
tbl.3.b.2 <- seq(2, 6 * 4, 4) %>%
map_df(~ fun.3.b(., tbl.3.b))
tbl.3.b.2 %>%
kable(col.names = c("attribute",
"intercept", "slope",
"intercept", "slope"),
digits = 3) %>%
kable_styling("striped", position = "left", full_width = F) %>%
add_header_above(c(" " = 1, "Men" = 2, "Women" = 2))
|
Men
|
Women
|
attribute
|
intercept
|
slope
|
intercept
|
slope
|
wacon
|
3.135
|
-0.111
|
3.261
|
-0.103
|
warel
|
3.553
|
-0.195
|
4.022
|
-0.245
|
wasec
|
3.220
|
-0.129
|
3.476
|
-0.139
|
facon
|
3.284
|
-0.128
|
4.187
|
-0.258
|
farel
|
3.138
|
-0.093
|
4.389
|
-0.281
|
fasec
|
3.323
|
-0.128
|
4.356
|
-0.283
|
Plot the simple intercepts and slopes
vec.3.b <- c('need', 'intercept', 'slope')
tbl.3.b.3 <- tbl.3.b.2 %>%
{list(men = select(., 1:3), women = select(., c(1, 4:5)))} %>%
map(~ set_colnames(., vec.3.b)) %>%
bind_rows() %>%
add_column(gen = factor(c(rep("male", 6), rep('female', 6))))
tbl.3.b.3 %>%
filter(grepl('fa', need)) %>%
mutate(new = paste(need, ifelse(gen == 'male',
'-m', '-f'), sep = '')) %>%
ggplot(aes(x = 1, y = intercept,
xend = 7, yend = intercept + slope * 7,
color = gen)) +
geom_segment() +
# geom_dl(aes(label = new, color = gen),
# method = list(dl.trans(x = x - 1.5), 'last.bumpup')) +
scale_x_continuous(expand = expand_scale(.25)) +
scale_y_continuous(expand = expand_scale(.1)) +
labs(x = "predictor", y = "anxiety", title = "Plot of Simple Slopes for Family-Related Predictors") +
scale_color_discrete(name = "gender")
## Warning: `expand_scale()` is deprecated; use `expansion()` instead.
## Warning: `expand_scale()` is deprecated; use `expansion()` instead.
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)
c. Moderation by Importance
Analysis of importance as a moderating variable of effects on anxiety.
Significant interactions are automatically highlighted with green text.
tbl.3.c.a <- tbl.3 %>%
names() %>%
grep('wa|fa', ., value = TRUE) %>%
map2(grep('wi|fi', names(tbl.3), value = TRUE),
~ paste('anx ~', .x, '+', .y, '+',
.x, '*', .y) %>% as.formula()) %>%
map_df(~ lm(., tbl.3) %>% tidy())
tbl.3.c.a %>%
mutate(estimate = cell_spec(round(estimate, 3), "html",
color = ifelse(grepl(':', term) &
(p.value < .05),
"green", "black"))) %>%
ks('Regression Output for Moderation by Importance')
Regression Output for Moderation by Importance
term
|
estimate
|
std.error
|
statistic
|
p.value
|
(Intercept)
|
2.034
|
0.500
|
4.067
|
0.000
|
wacon
|
0.032
|
0.113
|
0.283
|
0.777
|
wicon
|
0.185
|
0.068
|
2.735
|
0.006
|
wacon:wicon
|
-0.023
|
0.015
|
-1.588
|
0.112
|
(Intercept)
|
2.979
|
0.521
|
5.720
|
0.000
|
warel
|
-0.085
|
0.110
|
-0.771
|
0.441
|
wirel
|
0.126
|
0.071
|
1.762
|
0.078
|
warel:wirel
|
-0.02
|
0.015
|
-1.396
|
0.163
|
(Intercept)
|
2.721
|
0.431
|
6.315
|
0.000
|
wasec
|
-0.057
|
0.094
|
-0.606
|
0.545
|
wisec
|
0.077
|
0.049
|
1.587
|
0.113
|
wasec:wisec
|
-0.009
|
0.010
|
-0.858
|
0.391
|
(Intercept)
|
2.341
|
0.645
|
3.628
|
0.000
|
facon
|
0.039
|
0.130
|
0.301
|
0.763
|
ficon
|
0.208
|
0.081
|
2.558
|
0.011
|
facon:ficon
|
-0.034
|
0.016
|
-2.163
|
0.031
|
(Intercept)
|
2.668
|
0.620
|
4.304
|
0.000
|
farel
|
-0.052
|
0.134
|
-0.386
|
0.699
|
firel
|
0.168
|
0.072
|
2.339
|
0.019
|
farel:firel
|
-0.022
|
0.015
|
-1.528
|
0.127
|
(Intercept)
|
2.598
|
0.540
|
4.808
|
0.000
|
fasec
|
-0.019
|
0.116
|
-0.163
|
0.871
|
fisec
|
0.182
|
0.063
|
2.871
|
0.004
|
fasec:fisec
|
-0.028
|
0.013
|
-2.130
|
0.033
|
Compute the intercepts and slopes
fun.3.c <- function(i, t, data) {
v.e <- t[["estimate"]] # vector of coefficient estimates
v.t <- t[["term"]] # vector of terms
m.t <- v.t[[i + 1]] # name of moderator
m <- data[[m.t]] # vector of moderator data
s.m <- sd(m) # standard deviation of moderator
x.m <- mean(m) # mean of moderator
hi <- x.m + s.m # +1 SD level of moderator
med <- x.m # mean level of moderator
lo <- x.m - s.m # -1 SD level of moderator
int <- v.e[i - 1] # intercept estimate
me <- v.e[i] # main effect estimate
mo <- v.e[i + 1] # main effect of moderator
pr <- v.e[i + 2] # coeffient of product term estimate
s.h <- me + pr * hi # +1 SD: slope
i.h <- int + mo * hi # +1 SD: intercept
s.m <- me + pr * med # mean: slope
i.m <- int + mo * med # mean: int
s.l <- me + pr * lo # -1 SD: slope
i.l <- int + mo * lo # -1 SD: int
list(term = v.t[[i]], # result
int.low = i.l, slo.low = s.l,
int.med = i.m, slo.med = s.m,
int.hi = i.h, slo.hi = s.h)
}
tbl.3.c.2 <- seq(2, 6 * 4, 4) %>%
map_df(~ fun.3.c(., tbl.3.c.a, tbl.3))
headers <- c('Intercept', 'Slope')
tbl.3.c.2 %>%
kable(col.names = c("Attribute", rep(headers, 3)), digits = 3) %>%
kable_styling("striped", position = "left", full_width = F) %>%
add_header_above(c(" " = 1, "Low (-1 SD)" = 2, "Medium (Mean)" = 2, 'High (+1 SD)' = 2))
|
Low (-1 SD)
|
Medium (Mean)
|
High (+1 SD)
|
Attribute
|
Intercept
|
Slope
|
Intercept
|
Slope
|
Intercept
|
Slope
|
wacon
|
3.099
|
-0.102
|
3.375
|
-0.137
|
3.651
|
-0.172
|
warel
|
3.688
|
-0.199
|
3.889
|
-0.232
|
4.089
|
-0.264
|
wasec
|
3.245
|
-0.117
|
3.381
|
-0.133
|
3.518
|
-0.149
|
facon
|
3.639
|
-0.173
|
3.971
|
-0.227
|
4.303
|
-0.281
|
farel
|
3.949
|
-0.222
|
4.162
|
-0.251
|
4.376
|
-0.279
|
fasec
|
3.933
|
-0.221
|
4.186
|
-0.259
|
4.439
|
-0.298
|
Plot the simple intercepts and slopes
vec.3.c <- c('need', 'intercept', 'slope')
tbl.3.c.3 <- tbl.3.c.2 %>%
{list(low = select(., 1:3),
medium = select(., c(1, 4:5)),
high = select(., c(1, 6:7)))} %>%
map(~ set_colnames(., vec.3.b)) %>%
bind_rows() %>%
add_column(lvl = ordered(c(rep("low", 6),
rep('medium', 6),
rep('high', 6)),
levels = c('low', 'medium', 'high')))
tbl.3.c.3 %>%
filter(grepl('facon|fasec', need)) %>%
mutate(new = paste(need, ifelse(lvl == 'low', '-l',
ifelse(lvl == 'medium', '-m',
'-h')), sep = '')) %>%
ggplot(aes(x = 1, y = intercept,
xend = 7, yend = intercept + slope * 7,
color = lvl)) +
geom_segment() +
# geom_dl(aes(label = new, color = lvl),
# method = list(dl.trans(x = x - 1.5), 'last.bumpup')) +
scale_x_continuous(expand = expand_scale(.25)) +
scale_y_continuous(expand = expand_scale(.1)) +
labs(x = "predictor", y = "anxiety", title = "Plot of Simple Slopes for Significant Interactions with Importance") +
scale_color_discrete(name = "Level")
## Warning: `expand_scale()` is deprecated; use `expansion()` instead.
## Warning: `expand_scale()` is deprecated; use `expansion()` instead.
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)
ggsave("imp_simple.png", last_plot(), width = 6, height = 4.5, dpi = 600)