Robust Regression, Moderation, Mediation, and Nonlinear Regression
Kareena del Rosario
2024-03-28
To see a summary of the regression assumptions and more ways run test diagnostics, see our previous lab
pkgs <- c("tidyverse",
"dplyr",
"haven",
"foreign",
"lme4",
"nlme",
"lsr",
"emmeans",
"afex",
"knitr",
"kableExtra",
"car",
"mediation",
"rockchalk",
"multilevel",
"bda",
"gvlma",
"stargazer",
"QuantPsyc",
"pequod",
"MASS",
"texreg",
"pwr",
"effectsize",
"semPlot",
"lmtest",
"semptools",
"conflicted",
"nnet",
"ordinal",
"DescTools")
packages <- rownames(installed.packages())
p_to_install <- pkgs[!(pkgs %in% packages)]
if(length(p_to_install) > 0){
install.packages(p_to_install)
}
lapply(pkgs, library, character.only = TRUE)
# devtools::install_github("cardiomoon/semMediation")
library(semMediation)
# tell R which package to use for functions that are in multiple packages
these_functions <- c("mutate", "select", "summarize", "filter")
lapply(these_functions, conflict_prefer, "dplyr")
conflict_prefer("mutate", "dplyr")
conflict_prefer("select", "dplyr")
conflict_prefer("summarize", "dplyr")1 Quick check-in on homework 2
1.0.1 Power analysis for ANOVA and chi-square
1.0.1.1 ANOVA
# quick ANOVA for demonstration
# create id variable for error term
iris_afex <- iris %>%
dplyr::mutate(id = row_number())
anova_ex <- afex::aov_car(Sepal.Length ~ Species + Error(id), data = iris_afex)
summary(anova_ex)Anova Table (Type 3 tests)
Response: Sepal.Length
num Df den Df MSE F ges Pr(>F)
Species 2 147 0.26501 119.26 0.61871 < 0.00000000000000022 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Effect Size for ANOVA (Type III)
Parameter | Cohen's f | 95% CI
-----------------------------------
Species | 1.27 | [1.09, Inf]
- One-sided CIs: upper bound fixed at [Inf].1.0.1.2 Chi-square
# here is another power analysis function that allows you to use cohen's w.
library(pwr)
pwr.chisq.test(w=0.2,df=1,power=.95,sig.level=0.05)
Chi squared power calculation
w = 0.2
N = 324.8677
df = 1
sig.level = 0.05
power = 0.95
NOTE: N is the number of observations1.0.1.3 Regression
library(effectsize)
# Get f-squared
reg_ex <- lm(Sepal.Length ~ Species, data = iris_afex)
cohens_f_squared(reg_ex)# Effect Size for ANOVA
Parameter | Cohen's f2 | 95% CI
------------------------------------
Species | 1.62 | [1.18, Inf]
- One-sided CIs: upper bound fixed at [Inf].# Manually calculate f-squared
r_squared <- summary(reg_ex)$r.squared
f_squared <- r_squared / (1 - r_squared)
library(pwr)
power_analysis <- pwr.f2.test(u = 2, f2 = .15, sig.level = 0.05, power = 0.95)
print(power_analysis)
Multiple regression power calculation
u = 2
v = 103.0185
f2 = 0.15
sig.level = 0.05
power = 0.951.0.2 Planned contrasts vs pairwise comparisons
Gender (Male, Female) Film (Bridget Jones, Memento)
For people who watched Memento, do women report higher arousal after watching the film than men?
1.0.2.1 Planned contrasts
d.data <- read.delim("/Users/kareenadelrosario/Downloads/ChickFlick.dat")
d.data <- d.data %>%
mutate(gender = as.factor(ifelse(gender == "Female", 0, 1)),
film = as.factor(ifelse(film == "Memento", 0, 1)))
contrasts(d.data$gender) = contr.treatment(2, base = 2) # female = 1, male = 0
contrasts(d.data$film) # memento = 0, bridget jones = 1 1
0 0
1 1
Call:
lm(formula = arousal ~ gender * film, data = d.data)
Residuals:
Min 1Q Median 3Q Max
-10.700 -4.350 0.450 5.425 11.300
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 25.800 2.019 12.778 0.0000000000000061 ***
gender1 -1.100 2.856 -0.385 0.70234
film1 -8.600 2.856 -3.012 0.00473 **
gender1:film1 -3.700 4.038 -0.916 0.36564
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 6.385 on 36 degrees of freedom
Multiple R-squared: 0.4525, Adjusted R-squared: 0.4069
F-statistic: 9.92 on 3 and 36 DF, p-value: 0.000066111.0.2.2 Pairwise comparisons
contrast estimate SE df t.ratio p.value
gender0 film0 - gender1 film0 -1.1 2.86 36 -0.385 0.9803
gender0 film0 - gender0 film1 12.3 2.86 36 4.307 0.0007
gender0 film0 - gender1 film1 7.5 2.86 36 2.627 0.0582
gender1 film0 - gender0 film1 13.4 2.86 36 4.693 0.0002
gender1 film0 - gender1 film1 8.6 2.86 36 3.012 0.0234
gender0 film1 - gender1 film1 -4.8 2.86 36 -1.681 0.3483
P value adjustment: tukey method for comparing a family of 4 estimates 1.0.2.3 Why can’t I just filter out Bridget Jones?
d.data.f <- d.data %>%
filter(film == 0)
f_model <- lm(arousal ~ gender, data = d.data.f)
summary(f_model)
Call:
lm(formula = arousal ~ gender, data = d.data.f)
Residuals:
Min 1Q Median 3Q Max
-10.700 -5.050 -0.700 6.225 11.300
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 25.800 2.309 11.173 0.00000000158 ***
gender1 -1.100 3.265 -0.337 0.74
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 7.302 on 18 degrees of freedom
Multiple R-squared: 0.006265, Adjusted R-squared: -0.04894
F-statistic: 0.1135 on 1 and 18 DF, p-value: 0.74012 Robust Regression
credit: https://stats.oarc.ucla.edu/r/dae/robust-regression/
What is the difference between OLS and robust regression? When would you use one over the other?
2.1 Dealing with outliers using Hubert and bisquare weights
Robust regression is suitable for cases where you’d typically use OLS regression but encounter outliers or high leverage points that aren’t errors or from a different population. Instead of excluding these points or treating all data equally as in OLS regression, robust regression offers a middle ground by assigning different weights to observations based on their reliability. Essentially, it’s a weighted least squares approach that adjusts weights in response to the features of the data.
Terms to know:
- Residual: The difference between the predicted value (based on the regression equation) and the actual, observed value.
- Outlier: In linear regression, an outlier is an observation with large residual. In other words, it is an observation whose dependent-variable value is unusual given its value on the predictor variables. An outlier may indicate a sample peculiarity or may indicate a data entry error or other problem.
- Leverage: An observation with an extreme value on a predictor variable is a point with high leverage. Leverage is a measure of how far an independent variable deviates from its mean. High leverage points can have a great amount of effect on the estimate of regression coefficients.
- Influence: An observation is said to be influential if removing the observation substantially changes the estimate of the regression coefficients. Influence can be thought of as the product of leverage and outlierness.
- Cook’s distance (or Cook’s D): A measure that combines the information of leverage and residual of the observation. sid state crime murder pctmetro pctwhite pcths poverty single
1 1 ak 761 9.0 41.8 75.2 86.6 9.1 14.3
2 2 al 780 11.6 67.4 73.5 66.9 17.4 11.5
3 3 ar 593 10.2 44.7 82.9 66.3 20.0 10.7
4 4 az 715 8.6 84.7 88.6 78.7 15.4 12.1
5 5 ca 1078 13.1 96.7 79.3 76.2 18.2 12.5
6 6 co 567 5.8 81.8 92.5 84.4 9.9 12.12.1.0.1 Variables
- (sid) State ID
- (state) State name
- (crime) Violent crimes per 100,000 people
- (poverty) Percent of population living under poverty line
- (single) Percent of population that are single parents
- Total observations: 51
- crime ~ poverty + single
2.1.0.2 Run OLS
We will begin by running an OLS regression and looking at diagnostic plots examining residuals, fitted values, Cook’s distance, and leverage.
Call:
lm(formula = crime ~ poverty + single, data = cdata)
Residuals:
Min 1Q Median 3Q Max
-811.14 -114.27 -22.44 121.86 689.82
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1368.189 187.205 -7.308 0.0000000024786 ***
poverty 6.787 8.989 0.755 0.454
single 166.373 19.423 8.566 0.0000000000312 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 243.6 on 48 degrees of freedom
Multiple R-squared: 0.7072, Adjusted R-squared: 0.695
F-statistic: 57.96 on 2 and 48 DF, p-value: 0.00000000000015782.1.1 Identify outliers
From these plots, we can identify observations 9, 25, and 51 as possibly problematic to our model. We can look at these observations to see which states they represent.
sid state
9 9 fl
25 25 ms
51 51 dcDC, Florida and Mississippi have either high leverage or large residuals. We can display the observations that have relatively large values of Cook’s D. A conventional cut-off point is 4/n, where n is the number of observations in the data set.
d1 <- cooks.distance(ols) # captures influential observations
r <- stdres(ols) # computes standardized residuals
a <- cbind(cdata, d1, r)
a[d1 > 4/51, ] # Filters the combined data frame a to display only those observations for which Cook's distance is greater than 4/n. n = 51 sid state crime murder pctmetro pctwhite pcths poverty single d1 r
1 1 ak 761 9.0 41.8 75.2 86.6 9.1 14.3 0.1254750 -1.397418
9 9 fl 1206 8.9 93.0 83.5 74.4 17.8 10.6 0.1425891 2.902663
25 25 ms 434 13.5 30.7 63.3 64.3 24.7 14.7 0.6138721 -3.562990
51 51 dc 2922 78.5 100.0 31.8 73.1 26.4 22.1 2.6362519 2.616447Now we will look at the residuals. We will generate a new variable called absr1, which is the absolute value of the residuals (because the sign of the residual doesn’t matter). We then print the ten observations with the highest absolute residual values.
sid state crime murder pctmetro pctwhite pcths poverty single d1 r
25 25 ms 434 13.5 30.7 63.3 64.3 24.7 14.7 0.61387212 -3.562990
9 9 fl 1206 8.9 93.0 83.5 74.4 17.8 10.6 0.14258909 2.902663
51 51 dc 2922 78.5 100.0 31.8 73.1 26.4 22.1 2.63625193 2.616447
46 46 vt 114 3.6 27.0 98.4 80.8 10.0 11.0 0.04271548 -1.742409
26 26 mt 178 3.0 24.0 92.6 81.0 14.9 10.8 0.01675501 -1.460885
21 21 me 126 1.6 35.7 98.5 78.8 10.7 10.6 0.02233128 -1.426741
1 1 ak 761 9.0 41.8 75.2 86.6 9.1 14.3 0.12547500 -1.397418
31 31 nj 627 5.3 100.0 80.8 76.7 10.9 9.6 0.02229184 1.354149
14 14 il 960 11.4 84.0 81.0 76.2 13.6 11.5 0.01265689 1.338192
20 20 md 998 12.7 92.8 68.9 78.4 9.7 12.0 0.03569623 1.287087
rabs
25 3.562990
9 2.902663
51 2.616447
46 1.742409
26 1.460885
21 1.426741
1 1.397418
31 1.354149
14 1.338192
20 1.2870872.1.2 IRLS with Huber weights
Now let’s run our first robust regression. Robust regression is done by iterated re-weighted least squares (IRLS). The command for running robust regression is rlm in the MASS package. There are several weighting functions that can be used for IRLS. We are going to first use the Huber weights in this example. We will then look at the final weights created by the IRLS process. This can be very useful.
Call: rlm(formula = crime ~ poverty + single, data = cdata)
Residuals:
Min 1Q Median 3Q Max
-846.09 -125.80 -16.49 119.15 679.94
Coefficients:
Value Std. Error t value
(Intercept) -1423.0373 167.5899 -8.4912
poverty 8.8677 8.0467 1.1020
single 168.9858 17.3878 9.7186
Residual standard error: 181.8 on 48 degrees of freedomLet’s take a look at the weights of the top 15 largest residuals
hweights <- data.frame(state = cdata$state, resid = rr.huber$resid, weight = rr.huber$w)
hweights2 <- hweights[order(rr.huber$w), ]
hweights2[1:15, ] state resid weight
25 ms -846.08536 0.2889618
9 fl 679.94327 0.3595480
46 vt -410.48310 0.5955740
51 dc 376.34468 0.6494131
26 mt -356.13760 0.6864625
21 me -337.09622 0.7252263
31 nj 331.11603 0.7383578
14 il 319.10036 0.7661169
1 ak -313.15532 0.7807432
20 md 307.19142 0.7958154
19 ma 291.20817 0.8395172
18 la -266.95752 0.9159411
2 al 105.40319 1.0000000
3 ar 30.53589 1.0000000
4 az -43.25299 1.0000000We can see that roughly, as the absolute residual goes down, the weight goes up.
All observations not shown above have a weight of 1. In OLS regression, all cases have a weight of 1. Hence, the more cases in the robust regression that have a weight close to one, the closer the results of the OLS and robust regressions.
2.1.3 IRLS with bisquare weights
Next, let’s run the same model, but using the bisquare weighting function. Again, we can look at the weights.
Call: rlm(formula = crime ~ poverty + single, data = cdata, psi = psi.bisquare)
Residuals:
Min 1Q Median 3Q Max
-905.59 -140.97 -14.98 114.65 668.38
Coefficients:
Value Std. Error t value
(Intercept) -1535.3338 164.5062 -9.3330
poverty 11.6903 7.8987 1.4800
single 175.9303 17.0678 10.3077
Residual standard error: 202.3 on 48 degrees of freedom# if you need significance values. MASS doesn't trust p-values and won't report them.
# texreg(rr.bisquare, ci.force=TRUE)Here are the weights for the same 15 observations using bisquare weights
biweights <- data.frame(state = cdata$state, resid = rr.bisquare$resid, weight = rr.bisquare$w)
biweights2 <- biweights[order(rr.bisquare$w), ]
biweights2[1:15, ] state resid weight
25 ms -905.5931 0.007652565
9 fl 668.3844 0.252870542
46 vt -402.8031 0.671495418
26 mt -360.8997 0.731136908
31 nj 345.9780 0.751347695
18 la -332.6527 0.768938330
21 me -328.6143 0.774103322
1 ak -325.8519 0.777662383
14 il 313.1466 0.793658594
20 md 308.7737 0.799065530
19 ma 297.6068 0.812596833
51 dc 260.6489 0.854441716
50 wy -234.1952 0.881660897
5 ca 201.4407 0.911713981
10 ga -186.5799 0.924033113We can see that the weight given to Mississippi is dramatically lower using the bisquare weighting function than the Huber weighting function and the parameter estimates from these two different weighting methods differ.
When comparing the results of a regular OLS regression and a robust regression, if the results are very different, you will most likely want to use the results from the robust regression. Large differences suggest that the model parameters are being highly influenced by outliers. Different functions have advantages and drawbacks. Huber weights can have difficulties with severe outliers, and bisquare weights can have difficulties converging.
2.2 GLS for heteroscedasticity
Robust regression does not directly address heteroscedasticity. To account for heteroscedasticity or autocorrelation in GLS, you would typically need to specify a particular structure for the covariance matrix of the errors that reflects the nature of the heteroscedasticity or correlation you’re dealing with. In other words, what is driving the difference in variance?
Heteroskedasticity.
Check the residuals vs fitted plot to see if the line is curved. That would indicate heteroscedasticity
2.2.1 Breush Pagan Test
studentized Breusch-Pagan test
data: ols
BP = 7.6296, df = 2, p-value = 0.02204ggplot(cdata, aes(x = single, y = crime)) +
geom_point(aes(color = poverty), alpha = 0.5) + # Color points by poverty level
geom_smooth(method = "lm", formula = y ~ x, se = FALSE, color = "green") +
labs(x = "Single Parent Percentage", y = "Crime Rate",
title = "Crime Rate vs. Single Parent Percentage",
subtitle = "Colored by Poverty Level") +
theme_minimal()
2.2.1.1 Using weights in the GLS Model
# Let's say we find that as single-parent household % increases, crime variance increases. This suggests a proportional relationship between single-parent and crime, so we'll account for variance changes as a power function
glsModel <- gls(crime ~ poverty + single, data = cdata,
weights = varPower(form = ~ single))
summary(glsModel)Generalized least squares fit by REML
Model: crime ~ poverty + single
Data: cdata
AIC BIC logLik
680.0737 689.4297 -335.0368
Variance function:
Structure: Power of variance covariate
Formula: ~single
Parameter estimates:
power
1.848189
Coefficients:
Value Std.Error t-value p-value
(Intercept) -1215.4468 229.36175 -5.299257 0.0000
poverty 8.7081 8.10173 1.074840 0.2878
single 150.3019 23.44772 6.410087 0.0000
Correlation:
(Intr) povrty
poverty -0.055
single -0.892 -0.387
Standardized residuals:
Min Q1 Med Q3 Max
-2.1045268 -0.4871898 -0.1202581 0.5487129 3.3453653
Residual standard error: 2.563121
Degrees of freedom: 51 total; 48 residual# Plotting standardized residuals vs fitted values
plot(fitted(glsModel), residuals(glsModel, type = "normalized"),
xlab = "Fitted values", ylab = "Standardized Residuals")
abline(h = 0, lty = 2)
# Let's say that the variability in crime scores differs as a function of the state (could formally test with levene's test). We could account for that on the weights line. Note this doesn't work here because each state only has one entry.
glsModel2 <- gls(crime ~ poverty + single, data = cdata,
weights = varIdent(form = ~ 1 | state))
summary(glsModel2)Generalized least squares fit by REML
Model: crime ~ poverty + single
Data: cdata
AIC BIC logLik
689.3053 790.3501 -290.6526
Variance function:
Structure: Different standard deviations per stratum
Formula: ~1 | state
Parameter estimates:
ak al ar az ca
1.000000000000 2.048549058024 0.068085574850 0.576119727497 4.300623446230
co ct de fl ga
0.000005454337 2.461595107494 2.922156518667 9.754497652367 0.418252848397
hi ia id il in
1.615479026361 2.084911823269 0.267399898634 5.737528373745 0.600830252092
ks ky la ma md
2.097280314278 1.744754031846 2.671187574741 5.420342182435 6.481315070471
me mi mn mo ms
3.861041771601 0.039565313233 0.077530452236 2.998643425989 10.913292603298
mt nc nd ne nh
4.671621555841 2.174747057479 0.603570546230 1.539150720484 0.890348399478
nj nm nv ny oh
5.171393725120 0.000028911708 3.937796504993 4.388504628947 0.510888858428
ok or pa ri sc
0.029274306912 0.000004348616 1.489888746595 0.374030689892 3.728761133878
sd tn tx ut va
1.468792274624 1.769559166951 1.237389620521 0.226046963631 0.536417315386
vt wa wi wv wy
4.569384180392 0.645710065105 2.037106623757 3.747919048775 2.651974336771
dc
11.049378262028
Coefficients:
Value Std.Error t-value p-value
(Intercept) -1161.1918 0.007238506 -160418.7 0
poverty 19.6750 0.000208372 94422.5 0
single 126.7281 0.000529827 239187.5 0
Correlation:
(Intr) povrty
poverty -0.586
single -0.952 0.311
Standardized residuals:
Min Q1 Med Q3 Max
-1.0000071 -0.9999989 0.9999944 1.0000002 1.0000075
Residual standard error: 69.06124
Degrees of freedom: 51 total; 48 residual2.3 Generating robust CIs with bootstrapping
Bootstrapping can be helpful if you have a small sample or your data violate the regression assumptions and you want to get more accurate CI estimates. While this won’t correct for heterogeneity of variance, bootstrapping can be used to estimate robust standard errors for regression coefficients.
When to use bootstrapping:
- Assumptions are violated
- Sample size is small
- Presence of outliers
bootReg <- function(formula, data, indices) {
d <- data[indices, ] # Use 'indices' to create a subset dataframe 'd'
fit <- lm(formula, data = d)
return(coef(fit))
}
bootResults <- boot (statistic = bootReg, formula = crime ~ poverty + single, data = cdata, R = 2000)
# based on the bootstrapping, how biased are our estimates?
summary(bootResults)
Number of bootstrap replications R = 2000
original bootBias bootSE bootMed
1 -1368.1887 93.4373 336.521 -1364.583
2 6.7874 1.5695 10.896 8.219
3 166.3727 -10.2531 31.364 163.437
Call:
lm(formula = crime ~ poverty + single, data = cdata)
Residuals:
Min 1Q Median 3Q Max
-811.14 -114.27 -22.44 121.86 689.82
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1368.189 187.205 -7.308 0.0000000024786 ***
poverty 6.787 8.989 0.755 0.454
single 166.373 19.423 8.566 0.0000000000312 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 243.6 on 48 degrees of freedom
Multiple R-squared: 0.7072, Adjusted R-squared: 0.695
F-statistic: 57.96 on 2 and 48 DF, p-value: 0.0000000000001578# intercept (index = 1)
boot.ci(bootResults, type = "bca", index = 1) # bca = bias corrected and acceleratedBOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 2000 bootstrap replicates
CALL :
boot.ci(boot.out = bootResults, type = "bca", index = 1)
Intervals :
Level BCa
95% (-1764, -590 )
Calculations and Intervals on Original ScaleBOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 2000 bootstrap replicates
CALL :
boot.ci(boot.out = bootResults, type = "bca", index = 2)
Intervals :
Level BCa
95% (-16.145, 26.785 )
Calculations and Intervals on Original ScaleBOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 2000 bootstrap replicates
CALL :
boot.ci(boot.out = bootResults, type = "bca", index = 3)
Intervals :
Level BCa
95% (103.9, 214.5 )
Calculations and Intervals on Original Scale
Some BCa intervals may be unstableHow do these compare to the OLS confidence intervals?
2.5 % 97.5 %
(Intercept) -1744.58988 -991.78745
poverty -11.28529 24.86001
single 127.32029 205.425052.4 Your turn!
A study was carried out to explore the relationship between Aggression and several potential predicting factors in 666 children who had an older sibling.
Variables measured were:
- Parenting_Style (high score = bad parenting practices)
- Computer_ Games (high score = more time spent playing computer games)
- Television (high score = more time spent watching television)
- Diet (high score = the child has a good diet low in additives)
- Sibling_Aggression (high score = more aggression seen in their older sibling).
The data are in the file ChildAggression.dat.
- Run a multiple regression testing the effect of these variables, using “Aggression” as the DV.
- Obtain the standardized parameter estimates (aka standardized betas).
- Check whether the model meets the regression assumptions using both plots and formal tests: a. homoscedasticity b. multicollinearity c. independence (no autocorrelation in residuals)
- Report your results – how would you interpret the R-squared? Which variables significantly predicted aggression?
model <- lm(Aggression ~ Television + Computer_Games + Sibling_Aggression + Diet + Parenting_Style, data = df)
summary(model)
Call:
lm(formula = Aggression ~ Television + Computer_Games + Sibling_Aggression +
Diet + Parenting_Style, data = df)
Residuals:
Min 1Q Median 3Q Max
-1.12629 -0.15253 -0.00421 0.15222 1.17669
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.004988 0.011983 -0.416 0.677350
Television 0.032916 0.046057 0.715 0.475059
Computer_Games 0.142161 0.036920 3.851 0.000129 ***
Sibling_Aggression 0.081684 0.038780 2.106 0.035550 *
Diet -0.109054 0.038076 -2.864 0.004315 **
Parenting_Style 0.056648 0.014557 3.891 0.000110 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.3071 on 660 degrees of freedom
Multiple R-squared: 0.08258, Adjusted R-squared: 0.07563
F-statistic: 11.88 on 5 and 660 DF, p-value: 0.00000000005025 Television Computer_Games Sibling_Aggression Diet
0.03192490 0.15211518 0.08357717 -0.11503080
Parenting_Style
0.17735588 Residuals vs Fitted: is used to check the assumptions of linearity. If the residuals are spread equally around a horizontal line without distinct patterns (red line is approximately horizontal at zero), that is a good indication of having a linear relationship.
Normal Q-Q: is used to check the normality of residuals assumption. If the majority of the residuals follow the straight dashed line, then the assumption is fulfilled.
Scale-Location: is used to check the homoscedasticity of residuals (equal variance of residuals). If the residuals are spread randomly and the see a horizontal line with equally (randomly) spread points, then the assumption is fulfilled.
Residuals vs Leverage: is used to identify any influential value in our dataset. Influential values are extreme values that might influence the regression results when included or excluded from the analysis. Look for cases outside of a dashed line (if there is a concerning point, you’ll see red lines pop up).
Homoscedasticity: residuals vs fitted & bp
studentized Breusch-Pagan test
data: model
BP = 10.439, df = 5, p-value = 0.0637Multicollinearity
- If the largest VIF is greater 10, then there’s cause for concern
- If the average VIF is substantially greater than 1, the model may be biased
- Tolerance below 0.1 means there’s a serious problem
- Tolerance below 0.2 means there’s a potential problem
Television Computer_Games Sibling_Aggression Diet
1.435525 1.122719 1.132618 1.160466
Parenting_Style
1.494296 [1] 1.269125 Television Computer_Games Sibling_Aggression Diet
0.6966095 0.8906946 0.8829104 0.8617231
Parenting_Style
0.6692115 Independence
lag Autocorrelation D-W Statistic p-value
1 0.04218005 1.912808 0.286
Alternative hypothesis: rho != 0Skew
Call:
lm(formula = Aggression ~ Television + Computer_Games + Sibling_Aggression +
Diet + Parenting_Style, data = df)
Coefficients:
(Intercept) Television Computer_Games Sibling_Aggression
-0.004988 0.032916 0.142161 0.081684
Diet Parenting_Style
-0.109054 0.056648
ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance = 0.05
Call:
gvlma(x = model)
Value p-value Decision
Global Stat 62.8865 0.000000000000716982 Assumptions NOT satisfied!
Skewness 0.4924 0.482846201232194572 Assumptions acceptable.
Kurtosis 61.4485 0.000000000000004552 Assumptions NOT satisfied!
Link Function 0.3833 0.535842599337205128 Assumptions acceptable.
Heteroscedasticity 0.5623 0.453336961025912588 Assumptions acceptable.3 Centering, rescaling, standardizing, contrast coding your predictors
adapted from: https://advstats.psychstat.org/book/mregression/index.php
Note that you never HAVE to center/recode your predictors. It should never influence the test significance– just the interpretation of your intercept and coefficients.
- If you have continuous predictors, you can center.
- If you have categorical predictors, you can dummy code or effects code (see ANOVA labs for info).
- If you have predictors with different scales, you can standardize.
Let’s say we’re interested in the effects of high school GPA (h.gpa), SAT, and quality of recommendation letters (recommd) on college GPA (c.gpa).
c.gpa h.gpa SAT recommd
1 2.04 2.01 1070 5
2 2.56 3.40 1254 6
3 3.75 3.68 1466 6
4 1.10 1.54 706 4
5 3.00 3.32 1160 5
6 0.05 0.33 756 3par(mfrow=c(2,2))
plot(gpa_df$h.gpa, gpa_df$c.gpa)
plot(gpa_df$SAT, gpa_df$c.gpa)
plot(gpa_df$recommd, gpa_df$c.gpa)
# original model
gpaModel<- lm(c.gpa ~ h.gpa + SAT + recommd, data = gpa_df)
summary(gpaModel)
Call:
lm(formula = c.gpa ~ h.gpa + SAT + recommd, data = gpa_df)
Residuals:
Min 1Q Median 3Q Max
-1.0979 -0.4407 -0.0094 0.3859 1.7606
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.1532639 0.3229381 -0.475 0.636156
h.gpa 0.3763511 0.1142615 3.294 0.001385 **
SAT 0.0012269 0.0003032 4.046 0.000105 ***
recommd 0.0226843 0.0509817 0.445 0.657358
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.5895 on 96 degrees of freedom
Multiple R-squared: 0.3997, Adjusted R-squared: 0.381
F-statistic: 21.31 on 3 and 96 DF, p-value: 0.000000000116
How would you interpret these estimates?
3.0.0.1 Centering
# center separately
gpa_df$h.gpaC <- scale(gpa_df$h.gpa, center=TRUE, scale=FALSE) # mean center without rescaling
# shortcut
centeredModel<- lm(c.gpa~ h.gpaC + scale(SAT,scale=F) + scale(recommd,scale=F), data=gpa_df)
summary(centeredModel)
Call:
lm(formula = c.gpa ~ h.gpaC + scale(SAT, scale = F) + scale(recommd,
scale = F), data = gpa_df)
Residuals:
Min 1Q Median 3Q Max
-1.0979 -0.4407 -0.0094 0.3859 1.7606
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.9805000 0.0589476 33.598 < 0.0000000000000002 ***
h.gpaC 0.3763511 0.1142615 3.294 0.001385 **
scale(SAT, scale = F) 0.0012269 0.0003032 4.046 0.000105 ***
scale(recommd, scale = F) 0.0226843 0.0509817 0.445 0.657358
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.5895 on 96 degrees of freedom
Multiple R-squared: 0.3997, Adjusted R-squared: 0.381
F-statistic: 21.31 on 3 and 96 DF, p-value: 0.0000000001163.0.0.2 Standardizing
When predictors like GPA (typically on a 0 to 4 scale) and SAT scores (typically on a 400 to 1600 scale) are involved, their coefficients can be difficult to compare directly because a one-unit change means something very different for each predictor. Through standardization, however, we can remove the scales of the predictors and therefore make the coefficients relatively more comparable. We can standardize predictors only or both predictors and the outcome variable.
After standardization, the variable means are all 0 and variances are all 1. The beta coefficient (output), tells us how many standard deviations the predicted DV changes given one standard deviation change in the IV when the other IVs are held constant.
In R, scale() can also be used for standardization. Note that to skip the estimation of the intercept, one can add -1 in the regression model formular.
# same as above except we remove the scale = F statement
betaModel<-lm(scale(c.gpa) ~ scale(h.gpa) + scale(SAT) + scale(recommd)-1, data=gpa_df)
summary(betaModel)
Call:
lm(formula = scale(c.gpa) ~ scale(h.gpa) + scale(SAT) + scale(recommd) -
1, data = gpa_df)
Residuals:
Min 1Q Median 3Q Max
-1.46544 -0.58820 -0.01254 0.51510 2.34994
Coefficients:
Estimate Std. Error t value Pr(>|t|)
scale(h.gpa) 0.36285 0.10959 3.311 0.00131 **
scale(SAT) 0.35593 0.08751 4.067 0.0000968 ***
scale(recommd) 0.04528 0.10123 0.447 0.65568
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.7827 on 97 degrees of freedom
Multiple R-squared: 0.3997, Adjusted R-squared: 0.3812
F-statistic: 21.53 on 3 and 97 DF, p-value: 0.00000000009028Alternatively, you could feed your centered model through lm.beta() to get the betas without rerunning the model
h.gpaC scale(SAT, scale = F) scale(recommd, scale = F)
0.3628458 0.3559267 0.0452765 4 Moderation vs Mediation
moderation & mediation content was adapted from: https://ademos.people.uic.edu/Chapter14.html#
You can think of this distinction as mediation answers how two variables are related whereas moderation tells us it depends.
- Mediation analysis tests for a hypothetical causal relationship in which X -> Y, and the underlying mechanism can be explained by M.
- Moderation looks at the influence of Z on X->Y to test for when or under what conditions an effect occurs. Moderators can strengthen, weaken, or reverse the nature of a relationship.
Mediators describe the how or why of a (typically well-established) relationship between two other variables and are sometimes called intermediary variables since they often describe the process through which an effect occurs. This is also sometimes called an indirect effect. For instance, people with higher incomes tend to live longer but this effect is explained by the mediating influence of having access to better health care.
5 Moderation Analyses
Moderation tests whether a variable (Z) affects the direction and/or strength of the relation between an IV (X) and a DV (Y). In other words, moderation tests for interactions that affect WHEN relationships between variables occur. Moderators are conceptually different from mediators (when versus how/why) but some variables may be a moderator or a mediator depending on your question.
Like mediation, moderation assumes that there is little to no measurement error in the moderator variable and that the DV did not CAUSE the moderator.
Basic Moderation Model.
5.1 Example Moderation Data
In this example we’ll say we are interested in whether the relationship between the number of hours of sleep (X) a graduate student receives and the attention that they pay to this tutorial (Y) is influenced by their consumption of coffee (Z).
Here we create the moderation effect by making our DV (Y) the product of levels of the IV (X) and our moderator (Z).
set.seed(123)#Standardizes the numbers generated by rnorm
N <- 100 #Number of participants; graduate students
X.hours <- abs(rnorm(N, 6, 4)) #IV; Hours of sleep
X1 <- abs(rnorm(N, 60, 30)) #Adding some systematic variance for our DV
Z.coffee <- rnorm(N, 30, 8) #Moderator; Ounces of coffee consumed
Y.attn <- abs((-0.8*X.hours) * (0.2*Z.coffee) - 0.5*X.hours - 0.4*X1 + 10 + rnorm(N, 0, 3)) #DV; Attention Paid
Moddata <- data.frame(X.hours, X1, Z.coffee, Y.attn)
summary(Moddata) X.hours X1 Z.coffee Y.attn
Min. : 0.195 Min. : 1.597 Min. :15.95 Min. : 2.386
1st Qu.: 4.025 1st Qu.: 35.967 1st Qu.:25.75 1st Qu.: 30.155
Median : 6.247 Median : 53.225 Median :30.29 Median : 47.761
Mean : 6.483 Mean : 56.806 Mean :30.96 Mean : 47.763
3rd Qu.: 8.767 3rd Qu.: 74.035 3rd Qu.:36.11 3rd Qu.: 61.727
Max. :14.749 Max. :157.231 Max. :48.34 Max. :136.947 Moderation can be tested by looking for significant interactions between the moderating variable (Z) and the IV (X). It is important to mean center both your moderator and your IV to reduce multicollinearity and make interpretation easier. Centering can be done using the scale function, which subtracts the mean of a variable from each value in that variable.
#Moderation
fitMod <- lm(Y.attn ~ X.hours + Z.coffee + X.hours:Z.coffee, data = Moddata) #Model interacts IV & moderator
# Alternative formatting
# fitMod <- lm(Y.wake ~ X.hours*Z.coffee)
print_p(coef(summary(fitMod))) Estimate Std. Error t value Pr(>|t|)
(Intercept) 27.5216 10.4032 2.6455 0.0095
X.hours -2.0323 1.3796 -1.4732 0.1440
Z.coffee -0.4114 0.3075 -1.3381 0.1840
X.hours:Z.coffee 0.2338 0.0413 5.6563 0.00005.1.1 How would you interpret the coefficients and intercept?
5.2 Centering predictors
Sometimes our coefficients don’t make any sense. We can make the 0 meaningful by centering our predictors.
### Two ways to center
Moddata <- Moddata %>%
mutate(X.hoursC = X.hours - mean(X.hours),
Z.coffeeC = Z.coffee - mean(Z.coffee))
# Centering Data
X.hoursC <- scale(X.hours, center=TRUE, scale=FALSE) #Centering IV; hours of sleep
Z.coffeeC <- scale(Z.coffee, center=TRUE, scale=FALSE) #Centering moderator; coffee consumption
##################################
# Reanalyze with centered variables
fitModC <- lm(Y.attn ~ X.hoursC + Z.coffeeC + X.hoursC:Z.coffeeC, data = Moddata)
print_p(coef(summary(fitModC))) Estimate Std. Error t value Pr(>|t|)
(Intercept) 48.5444 1.1729 41.3899 0
X.hoursC 5.2081 0.3487 14.9358 0
Z.coffeeC 1.1044 0.1554 7.1083 0
X.hoursC:Z.coffeeC 0.2338 0.0413 5.6563 0
Call:
lm(formula = Y.attn ~ X.hoursC + Z.coffeeC + X.hoursC:Z.coffeeC,
data = Moddata)
Coefficients:
(Intercept) X.hoursC Z.coffeeC X.hoursC:Z.coffeeC
48.5444 5.2081 1.1044 0.2338
ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance = 0.05
Call:
gvlma(x = fitModC)
Value p-value Decision
Global Stat 7.68778 0.10371 Assumptions acceptable.
Skewness 5.97432 0.01452 Assumptions NOT satisfied!
Kurtosis 0.94082 0.33207 Assumptions acceptable.
Link Function 0.73540 0.39114 Assumptions acceptable.
Heteroscedasticity 0.03724 0.84698 Assumptions acceptable.#Data Summary
stargazer(fitModC, type="html", digits = 2, font.size = "footnotesize", title = "Sleep and Coffee on Attention")| Dependent variable: | |
| Y.attn | |
| X.hoursC | 5.21*** |
| (0.35) | |
| Z.coffeeC | 1.10*** |
| (0.16) | |
| X.hoursC:Z.coffeeC | 0.23*** |
| (0.04) | |
| Constant | 48.54*** |
| (1.17) | |
| Observations | 100 |
| R2 | 0.77 |
| Adjusted R2 | 0.76 |
| Residual Std. Error | 11.65 (df = 96) |
| F Statistic | 104.78*** (df = 3; 96) |
| Note: | p<0.1; p<0.05; p<0.01 |
#Plotting
ps <- plotSlopes(fitModC, plotx="X.hoursC", modx="Z.coffeeC", xlab = "Sleep", ylab = "Attention Paid", modxVals = "std.dev")
5.3 Interpreting Moderation Results
Our model shows a significant interaction between hours slept and coffee consumption on attention paid to this tutorial (b = .23, SE = .04, p < .001). However, we’ll need to unpack this interaction visually to get a better idea of what this means.
The rockchalk function will automatically plot the simple slopes (1 SD above and 1 SD below the mean) of the moderating effect.
- This figure shows that those who drank less coffee (the black line) paid more attention with the more sleep that they got last night but paid less attention overall that average (the blue line).
- Those who drank more coffee (the green line) paid more attention when they slept more as well and paid more attention than average.
- The difference in the slopes for those who drank more or less coffee shows that coffee consumption moderates the relationship between hours of sleep and attention paid.
5.4 Decomposing interactions
credit: https://stats.oarc.ucla.edu/r/seminars/interactions-r/#s2
You know that hours spent exercising improves weight loss, but how does it interact with effort?
This is a hypothetical study of weight loss for 900 participants in a year-long study of 3 different exercise programs, a jogging program, a swimming program, and a reading program which serves as a control activity. Variables include
- loss: weight loss (continuous), positive = weight loss, negative scores = weight gain
- hours: hours spent exercising (continuous)
- effort: effort during exercise (continuous), 0 = minimal physical effort and 50 = maximum effort
- gender: participant gender (binary)
- male=1
- female=2
dat <- read.csv("https://stats.idre.ucla.edu/wp-content/uploads/2019/03/exercise.csv")
dat$gender <- factor(dat$gender,labels=c("male","female"))5.4.1 Continuous by continuous
How do we interpret an interaction with continuous predictors? And what is extrapolating?
\(Weight\ Loss = b_0 + b_1Hours + b_2Effort + b_3Hours*Effort\)
Call:
lm(formula = loss ~ hours * effort, data = dat)
Residuals:
Min 1Q Median 3Q Max
-29.52 -10.60 -1.78 11.13 34.51
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.79864 11.60362 0.672 0.5017
hours -9.37568 5.66392 -1.655 0.0982 .
effort -0.08028 0.38465 -0.209 0.8347
hours:effort 0.39335 0.18750 2.098 0.0362 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 13.56 on 896 degrees of freedom
Multiple R-squared: 0.07818, Adjusted R-squared: 0.07509
F-statistic: 25.33 on 3 and 896 DF, p-value: 0.0000000000000009826Although we may think that the slope of Hours should be positive at levels of Effort, remember that in this case, Effort is zero. As we see in our data, this is improbable as the minimum value of effort is 12.95.
Min. 1st Qu. Median Mean 3rd Qu. Max.
12.95 26.26 29.63 29.66 33.10 44.08 What would we expect weight loss to look like at average effort?
$hours
[1] 2
$effort
[1] 30 hours effort emmean SE df lower.CL upper.CL
2 30 10.2 0.453 896 9.35 11.1
Confidence level used: 0.95 The results show that predicted weight loss is 10.2 pounds if we put in two hours of exercise and an effort level of 30; this seems reasonable. Let’s see what happens when we predict weight loss for two hours of exercise given an effort level of 0.
hours effort emmean SE df lower.CL upper.CL
2 0 -11 2.65 896 -16.1 -5.76
Confidence level used: 0.95 The predicted weight gain is now 11 pounds. Weird, right? This is an example of extrapolating, which means we are making predictions about our data beyond what the data can support. This is why we should always choose reasonable values of our predictors in order to interpret our data properly.
extrapolating
We know to choose reasonable values when predicting values. The same concept applies when decomposing an interaction. Our output suggests that Hours varies by levels of Effort. Since effort is continuous, we can choose an infinite set of values with which to fix effort.
For ease of presentation, we can use what’s called “spotlight analysis” (Aiken & West, 1991). To do a spotlight analysis, we’ll divide Effort into three levels: low, average, high.
$EffA = + (Effort) $
$Eff = $
$EffB = - (Effort) $
[1] 34.8[1] 29.7[1] 24.5Recall that our simple slope is the relationship of hours on weight loss fixed a particular values of effort. In R, we can obtain simple slopes using the function emtrends. We first create a list which incorporates the three values of effort we found above in preparation for spotlight analysis.
mylist <- list(effort=c(effbr,effr,effar))
emtrends(contcont, pairwise ~effort, var="hours",at=mylist, adjust="none")$emtrends
effort hours.trend SE df lower.CL upper.CL
24.5 0.261 1.352 896 -2.392 2.91
29.7 2.307 0.915 896 0.511 4.10
34.8 4.313 1.308 896 1.745 6.88
Confidence level used: 0.95
$contrasts
contrast estimate SE df t.ratio p.value
effort24.5 - effort29.7 -2.05 0.975 896 -2.098 0.0362
effort24.5 - effort34.8 -4.05 1.931 896 -2.098 0.0362
effort29.7 - effort34.8 -2.01 0.956 896 -2.098 0.0362All comparisons of simple slopes result in the same p-value as the interaction itself.
Based on the tests above, yes the maginitude of the slope is larger between “low” and “high” versus “medium” and “high”, but the two p-values are the same.
$hours
[1] 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0
$effort
[1] 24.5 29.7 34.8
The results suggest that hours spent exercising is only effective for weight loss if we put in more effort, which supports the rationale for high intensity interval training.
5.5 Continuous by Categorical
The research question here is, do men and women (W) differ in the relationship between Hours (X) and Weight loss? Here, we’re going to use dummy coding.
dat$gender <- relevel(dat$gender, ref="female")
contcat <- lm(loss~hours*gender,data=dat)
summary(contcat)
Call:
lm(formula = loss ~ hours * gender, data = dat)
Residuals:
Min 1Q Median 3Q Max
-27.118 -11.350 -1.963 10.001 42.376
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.335 2.731 1.221 0.222
hours 3.315 1.332 2.489 0.013 *
gendermale 3.571 3.915 0.912 0.362
hours:gendermale -1.724 1.898 -0.908 0.364
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 14.06 on 896 degrees of freedom
Multiple R-squared: 0.008433, Adjusted R-squared: 0.005113
F-statistic: 2.54 on 3 and 896 DF, p-value: 0.055235.5.0.1 Obtaining simple slopes by each level of the categorical moderator
Since our goal is to obtain simple slopes of Hours by gender we use emtrends. We do not use emmeans because this function gives us the predicted values rather than slopes.
gender hours.trend SE df lower.CL upper.CL
female 3.32 1.33 896 0.702 5.93
male 1.59 1.35 896 -1.063 4.25
Confidence level used: 0.95 A common misconception is that since the simple slope of Hours is significant for females but not males, we should have seen a significant interaction. However, the interaction tests the difference of the Hours slope for males and females and not whether each simple slope is different from zero (which is what we have from the output above).
To test the difference in slopes, we add pairwise ~ gender to tell the function that we want the pairwise difference in the simple slope of Hours for females versus males.
$emtrends
gender hours.trend SE df lower.CL upper.CL
female 3.32 1.33 896 0.702 5.93
male 1.59 1.35 896 -1.063 4.25
Confidence level used: 0.95
$contrasts
contrast estimate SE df t.ratio p.value
female - male 1.72 1.9 896 0.908 0.3639Recall from our summary table, this is exactly the same as the interaction, which verifies that we have in fact obtained the interaction coefficient.
$hours
[1] 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0
$gender
[1] "female" "male" 
Another common approach to plotting predicted values:
newdata <- expand.grid(hours = seq(0, 4, by = 0.4), gender = c("female", "male"))
prediction <- predict(contcat, newdata, interval="confidence", level = 0.95)
# combine
newdata <- cbind(newdata, prediction)
ggplot(newdata, aes(x = hours, y = fit, color = gender)) +
geom_line(size = 1) +
geom_point(size = 2, shape = 1, fill = "white") +
geom_ribbon(aes(ymin = lwr, ymax = upr, fill = gender), alpha = 0.2, color = NA) +
theme_minimal() +
scale_color_manual(values = c("#4878D0", "#D65F5F")) +
scale_fill_manual(values = c("#4878D0", "#D65F5F")) +
labs(
title = "Predicted Loss by Hours and Gender",
x = "Hours",
y = "Predicted Loss",
color = "Gender",
fill = "Gender"
)
5.5.0.2 In sum
- Predicted values are points on the graph.
- Simple effects or slopes are the difference between two predicted values (i.e., two points).
- Interactions are the difference between simple effects of slopes;
- for an interaction involving a continuous IV, it’s the difference of two slopes (i.e., two lines)
- for a categorical by categorical interaction, the interaction is the difference in the height of the bars in one group versus the difference of the heights in another group (a.k.a., difference of differences).
6 Mediation Analyses
The Baron & Kenny method is among the original methods for testing for mediation but tends to have low statistical power. We’re covering it here because it provides a very clear approach to establishing relationships between variables and is still occasionally requested by reviewers.
Mediation tests whether the effects of X (the independent variable) on Y (the dependent variable) operate through a third variable, M (the mediator). In this way, mediators explain the causal relationship between two variables or “how” the relationship works.
Basic Mediation Model.
c = the total effect of X on Y with no consideration of mediator variables
c'= the direct effect of X on Y after controlling for M
ab= the indirect effect of X on Y through M
The above shows the standard mediation model. Full mediation occurs when the effect of X on Y disappears with M in the model. Partial mediation occurs when the effect of X on Y decreases by a nontrivial amount (the actual amount is up for debate) with M in the model.
6.0.1 Example Mediation Data
In this example we’ll say we are interested in whether the number of hours since dawn (X) affect the subjective ratings of wakefulness (Y) 100 graduate students through the consumption of coffee (M).
Note that we are intentionally creating a mediation effect here (because statistics is always more fun if we have something to find) and we do so below by creating M so that it is related to X and Y so that it is related to M. This creates the causal chain for our analysis to parse.
#setwd("user location") #Working directory
set.seed(123) #Standardizes the numbers generated by rnorm; see Chapter 5
N <- 100 #Number of participants; graduate students
X.hours <- rnorm(N, 175, 7) #IV; hours since dawn
M.coffee <- 0.7*X.hours + rnorm(N, 0, 5) #Suspected mediator; coffee consumption
Y.wake <- 0.4*M.coffee + rnorm(N, 0, 5) #DV; wakefulness
Meddata <- data.frame(X.hours, M.coffee, Y.wake)6.1 Method 1: Baron & Kenny
This is the original 4-step method used to describe a mediation effect. Steps 1 and 2 use basic linear regression while steps 3 and 4 use multiple regression.
Now, let’s apply the Baron & Kenny method to our data:
The Steps:
- Estimate the relationship between X on Y (hours since dawn on degree
of wakefulness)
- Path “c” must be significantly different from 0; must have a total effect between the IV & DV
- Y ~ X = SIGNIFICANT
- Estimate the relationship between X on M (hours since dawn on coffee
consumption)
- Path “a” must be significantly different from 0; IV and mediator must be related.
- M ~ X = SIGNIFICANT
- Estimate the relationship between M on Y controlling for X (coffee
consumption on wakefulness, controlling for hours since dawn)
- Path “b” must be significantly different from 0; mediator and DV must be related.
- Y ~ M + X = SIGNIFICANT
- Estimate the relationship between Y on X controlling for M
(wakefulness on hours since dawn, controlling for coffee consumption)
- Should be non-significant and nearly 0.
- X ~ Y + M = NON-SIGNIFICANT
#1. Total Effect
fit <- lm(Y.wake ~ X.hours, data=Meddata)
#2. Path A (X on M)
fita <- lm(M.coffee ~ X.hours, data=Meddata)
#3. Path B (M on Y, controlling for X)
fitb <- lm(Y.wake ~ M.coffee + X.hours, data=Meddata)
#4. Reversed Path C (Y on X, controlling for M)
fitc <- lm(X.hours ~ Y.wake + M.coffee, data=Meddata)#Summary Table
stargazer::stargazer(fit, fita, fitb, fitc, type="html", digits = 2, font.size = "footnotesize",title = "Baron and Kenny Method")| Dependent variable: | ||||
| Y.wake | M.coffee | Y.wake | X.hours | |
| (1) | (2) | (3) | (4) | |
| Y.wake | -0.11 | |||
| (0.10) | ||||
| M.coffee | 0.42*** | 0.70*** | ||
| (0.10) | (0.08) | |||
| X.hours | 0.17** | 0.66*** | -0.11 | |
| (0.08) | (0.08) | (0.10) | ||
| Constant | 19.88 | 6.04 | 17.32 | 96.11*** |
| (14.26) | (13.42) | (13.16) | (9.28) | |
| Observations | 100 | 100 | 100 | 100 |
| R2 | 0.04 | 0.43 | 0.19 | 0.44 |
| Adjusted R2 | 0.03 | 0.43 | 0.18 | 0.43 |
| Residual Std. Error | 5.16 (df = 98) | 4.85 (df = 98) | 4.76 (df = 97) | 4.82 (df = 97) |
| F Statistic | 4.34** (df = 1; 98) | 75.31*** (df = 1; 98) | 11.72*** (df = 2; 97) | 38.39*** (df = 2; 97) |
| Note: | p<0.1; p<0.05; p<0.01 | |||
6.1.1 Interpreting Baron & Kenny Results
- Here we find that our total effect model shows a significant positive relationship between hours since dawn (X) and wakefulness (Y).
- Our Path A model shows that hours since dawn (X) is also positively related to coffee consumption (M).
- Our Path B model then shows that coffee consumption (M) positively predicts wakefulness (Y) when controlling for hours since dawn (X).
- Finally, wakefulness (Y) does not predict hours since dawn (X) when controlling for coffee consumption (M).
Since the relationship between hours since dawn and wakefulness is no longer significant when controlling for coffee consumption, this suggests that coffee consumption does in fact mediate this relationship. However, this method alone does not allow for a formal test of the indirect effect so we don’t know if the change in this relationship is truly meaningful.
There are two primary methods for formally testing the significance of the indirect test: the Sobel test & bootstrapping (covered under the mediation method). These are considered outdated, so we’re going to move onto our preferred method.
6.2 Method 2: The Mediation Package Method
This package uses the more recent bootstrapping method of Preacher & Hayes (2004) to address the power limitations of the Sobel Test. This method computes the point estimate of the indirect effect (ab) over a large number of random sample (typically 1000) so it does not assume that the data are normally distributed and is especially more suitable for small sample sizes than the Baron & Kenny method.
To run the mediate function, we will again need a model of our IV (hours since dawn), predicting our mediator (coffee consumption) like our Path A model above. We will also need a model of the direct effect of our IV (hours since dawn) on our DV (wakefulness), when controlling for our mediator (coffee consumption). When can then use mediate to repeatedly simulate a comparsion between these models and to test the significance of the indirect effect of coffee consumption.
# Path A
fitM <- lm(M.coffee ~ X.hours, data=Meddata) #IV on M; Hours since dawn predicting coffee consumption
# Total
fitY <- lm(Y.wake ~ X.hours + M.coffee, data=Meddata) #IV and M on DV; Hours since dawn and coffee predicting wakefulness
# Check skew
gvlma(fitM) #data is positively skewed; could log transform
Call:
lm(formula = M.coffee ~ X.hours, data = Meddata)
Coefficients:
(Intercept) X.hours
6.0449 0.6625
ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance = 0.05
Call:
gvlma(x = fitM)
Value p-value Decision
Global Stat 8.833 0.06542 Assumptions acceptable.
Skewness 6.314 0.01198 Assumptions NOT satisfied!
Kurtosis 1.219 0.26949 Assumptions acceptable.
Link Function 1.076 0.29959 Assumptions acceptable.
Heteroscedasticity 0.223 0.63674 Assumptions acceptable.
Call:
lm(formula = Y.wake ~ X.hours + M.coffee, data = Meddata)
Coefficients:
(Intercept) X.hours M.coffee
17.3218 -0.1118 0.4238
ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance = 0.05
Call:
gvlma(x = fitY)
Value p-value Decision
Global Stat 3.41844 0.4904 Assumptions acceptable.
Skewness 1.85648 0.1730 Assumptions acceptable.
Kurtosis 0.77788 0.3778 Assumptions acceptable.
Link Function 0.71512 0.3977 Assumptions acceptable.
Heteroscedasticity 0.06896 0.7929 Assumptions acceptable.
Causal Mediation Analysis
Quasi-Bayesian Confidence Intervals
Estimate 95% CI Lower 95% CI Upper p-value
ACME 0.2808 0.1437 0.42 <0.0000000000000002 ***
ADE -0.1133 -0.3116 0.09 0.258
Total Effect 0.1674 0.0208 0.34 0.028 *
Prop. Mediated 1.6428 0.5631 8.44 0.028 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Sample Size Used: 100
Simulations: 1000 
#Bootstrap
fitMedBoot <- mediate(fitM, fitY, boot=TRUE, sims=2000, treat="X.hours", mediator="M.coffee")
summary(fitMedBoot)
Causal Mediation Analysis
Nonparametric Bootstrap Confidence Intervals with the Percentile Method
Estimate 95% CI Lower 95% CI Upper p-value
ACME 0.280784 0.136681 0.43 <0.0000000000000002 ***
ADE -0.111790 -0.288539 0.09 0.254
Total Effect 0.168993 -0.000457 0.34 0.051 .
Prop. Mediated 1.661509 -1.369638 9.83 0.051 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Sample Size Used: 100
Simulations: 2000 
6.2.1 Interpreting Mediation Results
The mediate function gives us:
- Average Causal Mediation Effects (ACME)
- Average Direct Effects (ADE), our combined indirect and direct effects (Total Effect)
- the ratio of these estimates (Prop. Mediated)
The ACME here is the indirect effect of M (total effect - direct effect) and thus this value tells us if our mediation effect is significant. If ACME is significant, but ADE is not, then we have full mediation. If ADE is significant, but ACME is not, then we have no mediation.
In this case, our fitMed model again shows a significant effect of coffee consumption on the relationship between hours since dawn and feelings of wakefulness, (ACME = .28, p < .001) with no direct effect of hours since dawn (ADE = -0.11, p = .27) and significant total effect (p < .05).
We can then bootstrap this comparison to verify this result in fitMedBoot and again find a significant mediation effect (ACME = .28, p < .001) and no direct effect of hours since dawn (ADE = -0.11, p = .27). However, with increased power, this analysis no longer shows a significant total effect (p = .07).
6.3 Method 3: Mediation using lavaan
library(lavaan)
model <-"
Y.wake ~ a*X.hours + b*M.coffee
M.coffee ~ c*X.hours
#indirect effect
ind:=b*c
#total effect
total:=a+(b*c)
"medsem<-sem(model = model, data = Meddata, se="bootstrap")
summary(medsem,standardized=T,fit.measures=T,rsquare=T)lavaan 0.6.17 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 5
Number of observations 100
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Model Test Baseline Model:
Test statistic 78.650
Degrees of freedom 3
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -595.177
Loglikelihood unrestricted model (H1) -595.177
Akaike (AIC) 1200.354
Bayesian (BIC) 1213.380
Sample-size adjusted Bayesian (SABIC) 1197.589
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.000
P-value H_0: RMSEA <= 0.050 NA
P-value H_0: RMSEA >= 0.080 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Bootstrap
Number of requested bootstrap draws 1000
Number of successful bootstrap draws 999
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Y.wake ~
X.hours (a) -0.112 0.102 -1.101 0.271 -0.112 -0.136
M.coffee (b) 0.424 0.102 4.153 0.000 0.424 0.519
M.coffee ~
X.hours (c) 0.663 0.075 8.823 0.000 0.663 0.659
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Y.wake 21.945 2.699 8.130 0.000 21.945 0.805
.M.coffee 23.086 3.567 6.472 0.000 23.086 0.565
R-Square:
Estimate
Y.wake 0.195
M.coffee 0.435
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ind 0.281 0.075 3.762 0.000 0.281 0.342
total 0.169 0.092 1.836 0.066 0.169 0.206
7 Other types of mediation
7.1 Mediation with Categorical Predictors
When you have categorical predictors with more than 2 levels, you will need to model the mediation effects for each level of that variable. To do that, we’re going to dummy code our categorical variable. We’re going to use the same dataset but create a 3-level predictor: a lot of sleep, average sleep, little sleep. I know this would be considered ordinal, but let’s ignore that for now.
IMPORTANT NOTES:
- When dummy coding a categorical variable with K categories, include
only K−1 dummy variables in the model, treating one category as a
reference. This avoids the issue of perfect multicollinearity.
- If all dummy-coded variables for a categorical predictor are included in the model, this violates the assumption of independence because the sum of all dummy variables for a given observation is always 1 (if you include a dummy for each category). In other words, you’ll get perfect multicollinearity, where one variable can be perfectly predicted from the others, leading to issues in estimating the model parameters.
- The interpretation of these coefficients are now in reference to the excluded dummy (i.e., the reference category).
7.1.0.1 Lavaan
Here, the reference group will be the people who got ‘a lot’ of sleep (sleep=0)
# creating our dataset
set.seed(123)
N <- 100
# sleep: 0 = a lot, 1 = average, 2 = a little
X.sleep <- sample(0:2, N, replace = TRUE)
sleep_effect <- -2
M.coffee <- 0.7 * X.hours + sleep_effect * X.sleep + rnorm(N, 0, 5)
Y.wake <- 0.4 * M.coffee + rnorm(N, 0, 5)
Meddata_cat <- data.frame(X.hours, X.sleep, M.coffee, Y.wake)
Meddata_cat$sleep <- factor(Meddata_cat$X.sleep)
# dummy code sleep
library(fastDummies)
Meddata_cat <- dummy_cols(Meddata_cat,
select_columns = "X.sleep")
# 'a lot' of sleep is the reference category, so you can omit X.sleep_0 from the model
model_cat <-"
# Direct Effects on wakefulness
Y.wake ~ a1*X.sleep_1 + a2*X.sleep_2 + b*M.coffee
# Effect of sleep on coffee (note: now we use only two dummies, assuming one as reference)
M.coffee ~ c1*X.sleep_1 + c2*X.sleep_2
# Indirect effects (now must include dummy paths for only two levels)
ind1:=b*c1
ind2:=b*c2
# Total effects
total1 := a1 + (b*c1)
total2 := a2 + (b*c2)
"
med_cat<-sem(model = model_cat, data = Meddata_cat)
summary(med_cat,standardized=T,fit.measures=T,rsquare=T)lavaan 0.6.17 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 7
Number of observations 100
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Model Test Baseline Model:
Test statistic 49.270
Degrees of freedom 5
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -628.077
Loglikelihood unrestricted model (H1) -628.077
Akaike (AIC) 1270.155
Bayesian (BIC) 1288.391
Sample-size adjusted Bayesian (SABIC) 1266.283
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.000
P-value H_0: RMSEA <= 0.050 NA
P-value H_0: RMSEA >= 0.080 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Y.wake ~
X.sleep_1 (a1) -0.491 1.160 -0.423 0.672 -0.491 -0.042
X.sleep_2 (a2) -0.936 1.208 -0.775 0.438 -0.936 -0.081
M.coffee (b) 0.383 0.070 5.481 0.000 0.383 0.503
M.coffee ~
X.sleep_1 (c1) -0.180 1.660 -0.109 0.913 -0.180 -0.012
X.sleep_2 (c2) -5.957 1.624 -3.669 0.000 -5.957 -0.392
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Y.wake 21.848 3.090 7.071 0.000 21.848 0.718
.M.coffee 44.776 6.332 7.071 0.000 44.776 0.851
R-Square:
Estimate
Y.wake 0.282
M.coffee 0.149
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ind1 -0.069 0.636 -0.109 0.913 -0.069 -0.006
ind2 -2.281 0.748 -3.049 0.002 -2.281 -0.197
total1 -0.560 1.322 -0.423 0.672 -0.560 -0.047
total2 -3.217 1.293 -2.487 0.013 -3.217 -0.278
7.1.0.2 Mediation package
The process is similar when using the mediation, but note that you’ll need to run separate mediations for each level.
# Model predicting mediator (coffee)
model_mediator <- lm(M.coffee ~ X.sleep_1 + X.sleep_2, data = Meddata_cat)
# Model predicting outcome (wake), including mediator
model_outcome <- lm(Y.wake ~ X.sleep_1 + X.sleep_2 + M.coffee, data = Meddata_cat)
# average sleep vs a lot of sleep
med.1 <- mediate(model_mediator, model_outcome, treat = "X.sleep_1", mediator = "M.coffee")
summary(med.1)
Causal Mediation Analysis
Quasi-Bayesian Confidence Intervals
Estimate 95% CI Lower 95% CI Upper p-value
ACME -0.0714 -1.4659 1.19 0.93
ADE -0.4922 -2.8570 1.79 0.67
Total Effect -0.5636 -3.1142 2.05 0.66
Prop. Mediated 0.2188 -3.1517 4.22 0.68
Sample Size Used: 100
Simulations: 1000 # little sleep vs a lot of sleep
med.2 <- mediate(model_mediator, model_outcome, treat = "X.sleep_2", mediator = "M.coffee")
summary(med.2)
Causal Mediation Analysis
Quasi-Bayesian Confidence Intervals
Estimate 95% CI Lower 95% CI Upper p-value
ACME -2.283 -3.946 -0.97 <0.0000000000000002 ***
ADE -0.946 -3.331 1.51 0.46
Total Effect -3.228 -5.672 -0.76 0.01 **
Prop. Mediated 0.712 0.276 2.29 0.01 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Sample Size Used: 100
Simulations: 1000 7.2 Parallel Mediation
Meddata$M2.activity <- 2.1 * Meddata$X.hours + rnorm(nrow(Meddata), mean = 0, sd = 1)
summary(lm(Y.wake ~ M2.activity, data = Meddata))
Call:
lm(formula = Y.wake ~ M2.activity, data = Meddata)
Residuals:
Min 1Q Median 3Q Max
-10.7903 -3.7035 -0.2119 2.8524 12.5561
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 19.01365 14.47448 1.314 0.1920
M2.activity 0.08282 0.03921 2.112 0.0372 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 5.157 on 98 degrees of freedom
Multiple R-squared: 0.04353, Adjusted R-squared: 0.03377
F-statistic: 4.461 on 1 and 98 DF, p-value: 0.03723# Define the model for the outcome variable
parallelModel <- lm(Y.wake ~ X.hours + M.coffee + M2.activity, data = Meddata)
# Define the models for the mediator variables
medModel_coffee <- lm(M.coffee ~ X.hours, data = Meddata)
medModel_activity <- lm(M2.activity ~ X.hours, data = Meddata)
# Perform the mediation analysis for each mediator
mediation_coffee <- mediate(medModel_coffee, parallelModel,
treat = "X.hours", mediator = "M.coffee",
boot = TRUE, sims = 500)
mediation_activity <- mediate(medModel_activity, parallelModel,
treat = "X.hours", mediator = "M2.activity",
boot = TRUE, sims = 500)
# Summarize the mediation analysis results
summary(mediation_coffee)
Causal Mediation Analysis
Nonparametric Bootstrap Confidence Intervals with the Percentile Method
Estimate 95% CI Lower 95% CI Upper p-value
ACME 0.280 0.141 0.42 <0.0000000000000002 ***
ADE -0.394 -2.568 1.53 0.73
Total Effect -0.114 -2.277 1.84 0.86
Prop. Mediated -2.458 -3.849 2.55 0.86
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Sample Size Used: 100
Simulations: 500
Causal Mediation Analysis
Nonparametric Bootstrap Confidence Intervals with the Percentile Method
Estimate 95% CI Lower 95% CI Upper p-value
ACME 0.283 -1.627 2.29 0.80
ADE -0.394 -2.459 1.49 0.71
Total Effect -0.111 -0.295 0.08 0.22
Prop. Mediated -2.553 -104.088 46.85 0.87
Sample Size Used: 100
Simulations: 500 multipleMediation <- '
# Direct
Y.wake ~ b1 * M.coffee + b2 * M2.activity + c * X.hours
M.coffee ~ a1 * X.hours
M2.activity ~ a2 * X.hours
# Indirect
indirect1 := a1 * b1
indirect2 := a2 * b2
# Total
total := c + (a1 * b1) + (a2 * b2)
# Covariance between mediators
M.coffee ~~ M2.activity
'
fit_mult <- sem(model = multipleMediation, data = Meddata)
summary(fit_mult, fit.measures = TRUE, standardized = TRUE)lavaan 0.6.17 ended normally after 15 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 9
Number of observations 100
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Model Test Baseline Model:
Test statistic 605.568
Degrees of freedom 6
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -731.262
Loglikelihood unrestricted model (H1) -731.262
Akaike (AIC) 1480.523
Bayesian (BIC) 1503.970
Sample-size adjusted Bayesian (SABIC) 1475.545
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.000
P-value H_0: RMSEA <= 0.050 NA
P-value H_0: RMSEA >= 0.080 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Y.wake ~
M.coffee (b1) 0.422 0.098 4.326 0.000 0.422 0.517
M2.actvty (b2) 0.137 0.496 0.276 0.782 0.137 0.345
X.hours (c) -0.394 1.025 -0.384 0.701 -0.394 -0.479
M.coffee ~
X.hours (a1) 0.663 0.076 8.766 0.000 0.663 0.659
M2.activity ~
X.hours (a2) 2.063 0.015 138.745 0.000 2.063 0.997
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.M.coffee ~~
.M2.activity 0.254 0.455 0.559 0.576 0.254 0.056
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Y.wake 21.929 3.101 7.071 0.000 21.929 0.805
.M.coffee 23.086 3.265 7.071 0.000 23.086 0.565
.M2.activity 0.894 0.126 7.071 0.000 0.894 0.005
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
indirect1 0.280 0.072 3.880 0.000 0.280 0.341
indirect2 0.283 1.024 0.276 0.782 0.283 0.344
total 0.169 0.080 2.103 0.035 0.169 0.206multMed<-sem(model = multipleMediation, data = Meddata, se="bootstrap")
summary(multMed,standardized=T,fit.measures=T,rsquare=T)lavaan 0.6.17 ended normally after 15 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 9
Number of observations 100
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Model Test Baseline Model:
Test statistic 605.568
Degrees of freedom 6
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -731.262
Loglikelihood unrestricted model (H1) -731.262
Akaike (AIC) 1480.523
Bayesian (BIC) 1503.970
Sample-size adjusted Bayesian (SABIC) 1475.545
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.000
P-value H_0: RMSEA <= 0.050 NA
P-value H_0: RMSEA >= 0.080 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Bootstrap
Number of requested bootstrap draws 1000
Number of successful bootstrap draws 974
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Y.wake ~
M.coffee (b1) 0.422 0.099 4.245 0.000 0.422 0.517
M2.actvty (b2) 0.137 0.529 0.259 0.796 0.137 0.345
X.hours (c) -0.394 1.097 -0.359 0.720 -0.394 -0.479
M.coffee ~
X.hours (a1) 0.663 0.074 8.968 0.000 0.663 0.659
M2.activity ~
X.hours (a2) 2.063 0.013 164.862 0.000 2.063 0.997
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.M.coffee ~~
.M2.activity 0.254 0.440 0.578 0.563 0.254 0.056
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Y.wake 21.929 2.655 8.259 0.000 21.929 0.805
.M.coffee 23.086 3.552 6.500 0.000 23.086 0.565
.M2.activity 0.894 0.141 6.327 0.000 0.894 0.005
R-Square:
Estimate
Y.wake 0.195
M.coffee 0.435
M2.activity 0.995
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
indirect1 0.280 0.074 3.782 0.000 0.280 0.341
indirect2 0.283 1.092 0.259 0.796 0.283 0.344
total 0.169 0.093 1.810 0.070 0.169 0.206
mediationPlot(multMed, indirect = TRUE, whatLabels = "par", secondIndirect = TRUE) #standardized estimates
# Generate random ages between 18 and 65
Meddata$age <- round(runif(N, min = 18, max = 65))
covMediation <- '
# Direct paths
M.coffee ~ a1 * X.hours + age
M2.activity ~ a2 * X.hours + age
Y.wake ~ b1 * M.coffee + b2 * M2.activity + c * X.hours + age
# Covariance between mediators
M.coffee ~~ M2.activity
# Indirect effects
indirect1 := a1 * b1
indirect2 := a2 * b2
# Total effect
total := c + (a1 * b1) + (a2 * b2)
'
fit_cov <- sem(model = covMediation, data = Meddata)
summary(fit_cov, fit.measures = TRUE, standardized = TRUE) # Adds fit measures and standardized estimateslavaan 0.6.17 ended normally after 20 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 12
Number of observations 100
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Model Test Baseline Model:
Test statistic 606.331
Degrees of freedom 9
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -730.880
Loglikelihood unrestricted model (H1) -730.880
Akaike (AIC) 1485.760
Bayesian (BIC) 1517.022
Sample-size adjusted Bayesian (SABIC) 1479.123
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.000
P-value H_0: RMSEA <= 0.050 NA
P-value H_0: RMSEA >= 0.080 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
M.coffee ~
X.hours (a1) 0.662 0.076 8.747 0.000 0.662 0.658
age -0.008 0.039 -0.212 0.832 -0.008 -0.016
M2.activity ~
X.hours (a2) 2.063 0.015 138.629 0.000 2.063 0.998
age 0.002 0.008 0.248 0.804 0.002 0.002
Y.wake ~
M.coffee (b1) 0.424 0.097 4.357 0.000 0.424 0.519
M2.actvty (b2) 0.127 0.495 0.256 0.798 0.127 0.319
X.hours (c) -0.370 1.022 -0.363 0.717 -0.370 -0.451
age 0.030 0.037 0.808 0.419 0.030 0.072
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.M.coffee ~~
.M2.activity 0.257 0.455 0.565 0.572 0.257 0.057
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.M.coffee 23.076 3.263 7.071 0.000 23.076 0.565
.M2.activity 0.893 0.126 7.071 0.000 0.893 0.005
.Y.wake 21.787 3.081 7.071 0.000 21.787 0.800
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
indirect1 0.281 0.072 3.900 0.000 0.281 0.342
indirect2 0.261 1.021 0.256 0.798 0.261 0.318
total 0.172 0.080 2.138 0.033 0.172 0.209covMed<-sem(model = covMediation, data = Meddata, se="bootstrap")
semPaths(object = covMed, whatLabels = "std")
7.3 Mediation with binary outcomes
Lavaan automatically detects binary DVs. There’s no need to add any special arguments.
Create binary DV: Pass or fail
pass_threshold <- median(Meddata$Y.wake)
# Create binary DV 'pass_fail', where 1 = pass, 0 = fail
Meddata$pass_fail <- ifelse(Meddata$Y.wake > pass_threshold, 1, 0)binaryMediation <- '
# Direct paths to mediators
M.coffee ~ a1 * X.hours + age
M2.activity ~ a2 * X.hours + age
# Binary outcome path using logit
pass_fail ~ b1 * M.coffee + b2 * M2.activity + c * X.hours + age
# Covariance between mediators
M.coffee ~~ M2.activity
# Indirect effects
indirect1 := a1 * b1
indirect2 := a2 * b2
# Total effect
total := c + (a1 * b1) + (a2 * b2)
'
# Fitting the model with lavaan
fitBinary <- sem(model = binaryMediation, data = Meddata, estimator = "ML", se = "bootstrap", bootstrap = 1000)
summary(fitBinary, fit.measures = TRUE, standardized = TRUE)lavaan 0.6.17 ended normally after 37 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 12
Number of observations 100
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Model Test Baseline Model:
Test statistic 598.365
Degrees of freedom 9
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -500.302
Loglikelihood unrestricted model (H1) -500.302
Akaike (AIC) 1024.604
Bayesian (BIC) 1055.866
Sample-size adjusted Bayesian (SABIC) 1017.967
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.000
P-value H_0: RMSEA <= 0.050 NA
P-value H_0: RMSEA >= 0.080 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Bootstrap
Number of requested bootstrap draws 1000
Number of successful bootstrap draws 1000
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
M.coffee ~
X.hours (a1) 0.662 0.075 8.806 0.000 0.662 0.658
age -0.008 0.039 -0.209 0.835 -0.008 -0.016
M2.activity ~
X.hours (a2) 2.063 0.012 167.090 0.000 2.063 0.998
age 0.002 0.009 0.217 0.829 0.002 0.002
pass_fail ~
M.coffee (b1) 0.030 0.009 3.221 0.001 0.030 0.386
M2.actvty (b2) 0.024 0.057 0.420 0.674 0.024 0.630
X.hours (c) -0.055 0.118 -0.468 0.640 -0.055 -0.701
age 0.005 0.004 1.394 0.163 0.005 0.130
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.M.coffee ~~
.M2.activity 0.257 0.423 0.608 0.544 0.257 0.057
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.M.coffee 23.076 3.691 6.251 0.000 23.076 0.565
.M2.activity 0.893 0.141 6.318 0.000 0.893 0.005
.pass_fail 0.216 0.016 13.747 0.000 0.216 0.866
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
indirect1 0.020 0.007 3.066 0.002 0.020 0.254
indirect2 0.049 0.118 0.420 0.674 0.049 0.628
total 0.014 0.008 1.848 0.065 0.014 0.182binMed<-sem(model = fitBinary, data = Meddata, se="bootstrap")
# basic
semPaths(object = binMed, whatLabels = "std")
# change shape and label size
binSem <- semPaths(binMed,
whatLabels = "std",
edge.label.cex = 0.75,
label.cex = 1.5,
layout = "spring")
Add labels
# change node label
binMed_lab <- change_node_label(binSem,
c(X.h = "Hours",
M.c = "Coffee",
M2. = "Activity",
ps_ = "Grade"),
label.cex = 1.1)
plot(binMed_lab)
Indicate which effects are significant
7.4 Moderated mediation
credit: https://ademos.people.uic.edu/Chapter15.html#31_describe_the_dataset
These are challenging to understand, so we’re going to walk through a different example.
Let’s examine the question: does spending more time in grad school predict more offers after graduation? We’ll see if this relationship is explained by number of publications (i.e., the more time spent in grad school, the more publications one has, and the more publications one has, the more job offers they get). However, this causal chain may only work for people who spend their time in graduate school networking.
We are going to simulate a dataset that measured the following:
- X = Time spent in graduate school (we will change the name to “time” when we create the data frame)
- Z = Time spent networking
- M = Number of publications in grad school
- Y = Number of job offers
### We are intentionally creating a moderated mediation effect here and we do so below by setting the relationships (the paths) between our causal chain variables and setting the relationships for our interaction terms
set.seed(42) #This makes sure that everyone gets the same numbers generated through rnorm function
a1 = -.59 #Set the path a1 strength (effect of X on M)
a2 = -.17 #Set path a2 strength (effect of Z on M)
a3 = .29 #Set path a3 strength (interaction between X and Z on M)
b = .59 #Set path b strength (effect of M on Y)
cdash1 = .27 #Set path c'1 strength (effect of X on Y)
cdash2 = .01 #Set path c'2 strength (effect of Z on Y)
cdash3 = -.01 #Set path c'3 strength (interaction betwee X and Z on Y)
### Here we are creating the values of our variables for each subject
n <- 200 #Set sample size
X <- rnorm(n, 7, 1) #IV: Time spent in grad school (M = 7, SD = 1)
Z <- rnorm(n, 5, 1) #Moderator: Time spent (hours per week) with Professor Demos in class or in office hours (M = 5, SD = 1)
M <- a1*X + a2*Z + a3*X*Z + rnorm(n, 0, .1) #Mediator: Number of publications in grad school
#The mediator variable is created as a function of the IV, moderator, and their interaction with some random noise thrown in the mix
Y <- cdash1*X + cdash2*Z + cdash3*X*Z + b*M + rnorm(n, 0, .1) #DV: Number of job offers
#Similar to the mediator, the DV is a function of the IV, moderator, their interaction, and the mediator with some random noise thrown in the mix
Success.ModMed <- data.frame(jobs = Y, time = X, pubs = M, network = Z) #Build our data frame and give it recognizable variable namesBecause we have interaction terms in our regression analyses, we need to mean center our IV and Moderator (Z)
Success.ModMed$time.c <- scale(Success.ModMed$time, center = TRUE, scale = FALSE)[,] #Scale returns a matrix so we have to make it a vector by indexing one column
Success.ModMed$network.c <- scale(Success.ModMed$network, center = TRUE, scale = FALSE)[,]Mod.Med.Lavaan <- '
#Regressions
#These are the same regression equations from our previous example
#Except in this code we are naming the coefficients that are produced from the regression equations
#E.g., the regression coefficient for the effect of time on pubs is named "a1"
pubs ~ a1*time.c + a2*network.c + a3*time.c:network.c
jobs ~ cdash1*time.c + cdash2*network.c + cdash3*time.c:network.c + b1*pubs
#Mean of centered network (for use in simple slopes)
#This is making a coefficient labeled "network.c.mean" which equals the intercept because of the "1"
#(Y~1) gives you the intercept, which is the mean for our network.c variable
network.c ~ network.c.mean*1
#Variance of centered network (for use in simple slopes)
#This is making a coefficient labeled "network.c.var" which equals the variance
#Two tildes separating the same variable gives you the variance
network.c ~~ network.c.var*network.c
#Indirect effects conditional on moderator (a1 + a3*ModValue)*b1
indirect.SDbelow := (a1 + a3*(network.c.mean-sqrt(network.c.var)))*b1
indirect.SDabove := (a1 + a3*(network.c.mean+sqrt(network.c.var)))*b1
#Direct effects conditional on moderator (cdash1 + cdash3*ModValue)
#We have to do it this way because you cannot call the mean and sd functions in lavaan package
direct.SDbelow := cdash1 + cdash3*(network.c.mean-sqrt(network.c.var))
direct.SDabove := cdash1 + cdash3*(network.c.mean+sqrt(network.c.var))
#Total effects conditional on moderator
total.SDbelow := direct.SDbelow + indirect.SDbelow
total.SDabove := direct.SDabove + indirect.SDabove
#Proportion mediated conditional on moderator
#To match the output of "mediate" package
prop.mediated.SDbelow := indirect.SDbelow / total.SDbelow
prop.mediated.SDabove := indirect.SDabove / total.SDabove
#Index of moderated mediation
#An alternative way of testing if conditional indirect effects are significantly different from each other
index.mod.med := a3*b1
'
#Fit model
Mod.Med.SEM <- sem(model = Mod.Med.Lavaan,
data = Success.ModMed,
se = "bootstrap",
bootstrap = 10,
fixed.x = FALSE) # pubs should model the variance
#Fit measures
summary(Mod.Med.SEM,
fit.measures = FALSE,
standardize = TRUE,
rsquare = TRUE)lavaan 0.6.17 ended normally after 51 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 18
Number of observations 200
Model Test User Model:
Test statistic 12.599
Degrees of freedom 2
P-value (Chi-square) 0.002
Parameter Estimates:
Standard errors Bootstrap
Number of requested bootstrap draws 10
Number of successful bootstrap draws 10
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
pubs ~
time.c (a1) 0.858 0.006 138.664 0.000 0.858 0.425
ntwrk.c (a2) 1.854 0.006 309.044 0.000 1.854 0.892
tm.c:n. (a3) 0.309 0.010 30.402 0.000 0.309 0.149
jobs ~
time.c (cds1) 0.219 0.051 4.339 0.000 0.219 0.175
ntwrk.c (cds2) -0.048 0.104 -0.462 0.644 -0.048 -0.037
tm.c:n. (cds3) -0.009 0.017 -0.556 0.578 -0.009 -0.007
pubs (b1) 0.584 0.057 10.308 0.000 0.584 0.942
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
time.c ~~
time.c:ntwrk.c -0.008 0.127 -0.062 0.951 -0.008 -0.009
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ntwrk.c (nt..) -0.000 0.084 -0.000 1.000 -0.000 -0.000
.pubs 5.163 0.007 723.506 0.000 5.163 2.629
.jobs 1.602 0.292 5.480 0.000 1.602 1.316
time.c 0.000 0.091 0.000 1.000 0.000 0.000
tm.c:n. -0.074 0.041 -1.809 0.070 -0.074 -0.078
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ntwrk.c (nt..) 0.892 0.050 17.959 0.000 0.892 1.000
.pubs 0.010 0.001 11.043 0.000 0.010 0.003
.jobs 0.009 0.001 11.307 0.000 0.009 0.006
time.c 0.945 0.075 12.565 0.000 0.945 1.000
tm.c:n. 0.889 0.136 6.513 0.000 0.889 1.000
R-Square:
Estimate
pubs 0.997
jobs 0.994
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
indirect.SDblw 0.330 0.036 9.182 0.000 0.330 0.260
indirect.SDabv 0.672 0.061 11.090 0.000 0.672 0.540
direct.SDbelow 0.228 0.040 5.704 0.000 0.228 0.182
direct.SDabove 0.210 0.068 3.101 0.002 0.210 0.168
total.SDbelow 0.559 0.014 41.333 0.000 0.559 0.443
total.SDabove 0.882 0.017 51.107 0.000 0.882 0.708
prp.mdtd.SDblw 0.591 0.067 8.771 0.000 0.591 0.588
prop.mdtd.SDbv 0.762 0.075 10.201 0.000 0.762 0.763
index.mod.med 0.181 0.019 9.693 0.000 0.181 0.140- pubs ~
- A1 (M ~ X): Significant main effect of time spent in grad school on number of publications
- A2 (M ~ Z): Significant main effect of time spent networking on number of publications
- A3 (M ~ X * Z): Significant interaction between time spent in grad school and time spent networking on number of publications
- jobs ~
- (cds1) (Y ~ X): Significant main effect of time spent in grad school on number of job offers
- (cds2) (Y ~ Z): No effect of time spent networking on number of job offers
- (cds3) (Y ~ M): Significant main effect of number of publications on number of job offers
- (b1) (Y ~ X * Z): No interaction between time spent in grad school and time spent networking on number of job offers
To look at the moderator effect, we can use the +/- 1SD from the mean
- those who spend little time networking
- (direct.SDblw) Significant direct effect of time spent in grad school on job offers (for those who don’t spend a lot of time networking)
- (indirect.SDbelow) Significant indirect effect of time spent in grad school on job offers through publications (for those who don’t spend a lot of time networking)
- those who spend a lot of time networking
- (direct.SDabv) Significant direct effect of time spent in grad school on job offers (for those who spend a lot of time networking)
- (indirect.SDabv) Significant indirect effect of time spent in grad school on job offers through publications (for those who spend a lot of time networking)
- what does this mean?
- Time spent in graduate school positively affects the number of job offers, both directly and indirectly through the number of publications. The strength of this indirect effect is depends on the amount of time spent networking.
- Specifically, while the mediated path was significant regardless of networking time, the strength of the publications explaining the relationship between time spent in grad school and job offers was stronger for people who spent a lot of time networking.
mm_plot <- semPaths(Mod.Med.SEM,
whatLabels = "est",
edge.label.cex = 0.75,
label.cex = 1.5,
layout = "spring",
intercepts = FALSE)
# change node label
Modmed_lab <- change_node_label(mm_plot,
c(jbs = "Y.Jobs",
pbs = "M.Pubs",
tm. = "X.Time",
nt. = "Z.Network",
't.:' = "T*N"),
label.cex = 1.1)
sig_plot_mm <- Modmed_lab %>%
mark_sig(Mod.Med.SEM) %>%
mark_se(Mod.Med.SEM, sep = "\n")
plot(sig_plot_mm)
#Bootstraps
parameterEstimates(Mod.Med.SEM,
boot.ci.type = "bca.simple",
level = .95, ci = TRUE,
standardized = FALSE)[c(19:27),c(4:10)] #We index the matrix to only display columns we are interested in label est se z pvalue ci.lower ci.upper
19 indirect.SDbelow 0.330 0.036 9.182 0.000 0.287 0.395
20 indirect.SDabove 0.672 0.061 11.090 0.000 0.571 0.749
21 direct.SDbelow 0.228 0.040 5.704 0.000 0.156 0.273
22 direct.SDabove 0.210 0.068 3.101 0.002 0.117 0.296
23 total.SDbelow 0.559 0.014 41.333 0.000 0.544 0.589
24 total.SDabove 0.882 0.017 51.107 0.000 0.864 0.921
25 prop.mediated.SDbelow 0.591 0.067 8.771 0.000 0.523 0.715
26 prop.mediated.SDabove 0.762 0.075 10.201 0.000 0.678 0.865
27 index.mod.med 0.181 0.019 9.693 0.000 0.155 0.208The difference is most likely a result of bootstrap estimation differences (e.g., lavaan uses bias-corrected but not accelerated bootstrapping for their confidence intervals)
#install.packages("JSmediation")
library(JSmediation)
Success.ModMed$pubs.c <- scale(Success.ModMed$pubs, center = TRUE, scale = FALSE)[,]
moderated_mediation_fit <-
mdt_moderated(data = Success.ModMed,
IV = time.c,
DV = jobs,
M = pubs.c,
Mod = network.c)
moderated_mediation_fit %>% add_index(stage = "first")Test of mediation (moderated mediation)
==============================================
Variables:
- IV: time.c
- DV: jobs
- M: pubs.c
- Mod: network.c
Paths:
======== ============== ===== =========================
Path Point estimate SE APA
======== ============== ===== =========================
a 0.858 0.008 t(196) = 114.12, p < .001
a * Mod 0.309 0.008 t(196) = 38.91, p < .001
b 0.584 0.065 t(194) = 8.99, p < .001
b * Mod -0.003 0.003 t(194) = 1.20, p = .233
c 0.720 0.008 t(196) = 88.82, p < .001
c * Mod 0.171 0.009 t(196) = 19.96, p < .001
c' 0.222 0.056 t(194) = 3.96, p < .001
c' * Mod -0.008 0.021 t(194) = 0.37, p = .709
======== ============== ===== =========================
Indirect effect index:
- type: Mediated moderation index (First stage)
- point estimate: 0.18
- confidence interval:
- method: Monte Carlo (5000 iterations)
- level: 0.05
- CI: [0.139; 0.221]
Fitted models:
- X * Mod -> Y
- X * Mod -> M
- (X + M) * Mod -> Y - type: Conditional simple mediation index (Mod = 1)
- point estimate: 0.677
- confidence interval:
- method: Monte Carlo (5000 iterations)
- level: 0.05
- CI: [0.526; 0.832]8 Nonlinear regression
This dataset has a binary response (outcome, dependent) variable called admit. There are three predictor variables: gre, gpa and rank. We will treat the variables gre and gpa as continuous. The variable rank takes on the values 1 through 4. Institutions with a rank of 1 have the highest prestige, while those with a rank of 4 have the lowest.
mydata <- read.csv("https://stats.idre.ucla.edu/stat/data/binary.csv")
xtabs(~admit + rank, data = mydata) rank
admit 1 2 3 4
0 28 97 93 55
1 33 54 28 128.1 Logistic regression
mydata$rank <- factor(mydata$rank)
mylogit <- glm(admit ~ gre + gpa + rank, data = mydata, family = "binomial")
summary(mylogit)
Call:
glm(formula = admit ~ gre + gpa + rank, family = "binomial",
data = mydata)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.6268 -0.8662 -0.6388 1.1490 2.0790
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -3.989979 1.139951 -3.500 0.000465 ***
gre 0.002264 0.001094 2.070 0.038465 *
gpa 0.804038 0.331819 2.423 0.015388 *
rank2 -0.675443 0.316490 -2.134 0.032829 *
rank3 -1.340204 0.345306 -3.881 0.000104 ***
rank4 -1.551464 0.417832 -3.713 0.000205 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 499.98 on 399 degrees of freedom
Residual deviance: 458.52 on 394 degrees of freedom
AIC: 470.52
Number of Fisher Scoring iterations: 4- For every one unit change in gre, the log odds of admission (versus non-admission) increases by 0.002.
- For a one unit increase in gpa, the log odds of being admitted to graduate school increases by 0.804.
- The indicator variables for rank have a slightly different interpretation. For example, having attended an undergraduate institution with rank of 2, versus an institution with a rank of 1, changes the log odds of admission by -0.675.
2.5 % 97.5 %
(Intercept) -6.2716202334 -1.792547080
gre 0.0001375921 0.004435874
gpa 0.1602959439 1.464142727
rank2 -1.3008888002 -0.056745722
rank3 -2.0276713127 -0.670372346
rank4 -2.4000265384 -0.753542605 OR 2.5 % 97.5 %
(Intercept) 0.0185001 0.001889165 0.1665354
gre 1.0022670 1.000137602 1.0044457
gpa 2.2345448 1.173858216 4.3238349
rank2 0.5089310 0.272289674 0.9448343
rank3 0.2617923 0.131641717 0.5115181
rank4 0.2119375 0.090715546 0.47069618.1.1 Wald-test (like an omnibus test)
Main effect of rank
Wald test:
----------
Chi-squared test:
X2 = 20.9, df = 3, P(> X2) = 0.00011The chi-squared test statistic of 20.9, with three degrees of freedom is associated with a p-value of 0.00011 indicating that the overall effect of rank is statistically significant.
Main effect of gre
Wald test:
----------
Chi-squared test:
X2 = 4.3, df = 1, P(> X2) = 0.038Main effect of gpa
Wald test:
----------
Chi-squared test:
X2 = 5.9, df = 1, P(> X2) = 0.0158.1.2 Graph logistic regression
- Start by calculating the predicted probability of the outcome at each level of the categorical/ordinal predictor variable and/or holding continuous variables at their means.
- Create the predicted probabilities using the new dataframe.
- Start creating the predicted probability version of your variables
- Set the SE to display
- Graph
# step 1
newdata1 <- with(mydata,
data.frame(gre = mean(gre), gpa = mean(gpa), rank = factor(1:4)))
# step 2
newdata1$rankP <- predict(mylogit, newdata = newdata1, type = "response")
newdata1 gre gpa rank rankP
1 587.7 3.3899 1 0.5166016
2 587.7 3.3899 2 0.3522846
3 587.7 3.3899 3 0.2186120
4 587.7 3.3899 4 0.1846684# step 3
newdata2 <- with(mydata,
data.frame(gre = rep(seq(from = 200, to = 800, length.out = 100), 4),
gpa = mean(gpa), rank = factor(rep(1:4, each = 100))))
# step 4
newdata3 <- cbind(newdata2, predict(mylogit, newdata = newdata2, type="link", se=TRUE))
newdata3 <- within(newdata3, {
PredictedProb <- plogis(fit)
LL <- plogis(fit - (1.96 * se.fit))
UL <- plogis(fit + (1.96 * se.fit))
})
# graph
PredProbPlot <- ggplot(newdata3, aes(x = gre, y = PredictedProb)) +
geom_ribbon(aes(ymin = LL, ymax = UL, fill = rank), alpha = .2) +
geom_line(aes(colour = rank), size=1) +theme_minimal()
PredProbPlot + ggtitle("Admission to Grad School by Rank")
8.2 Multinomial Regression
The data set contains variables on 200 students. The outcome variable is prog, program type. The predictor variables are social economic status, ses, a three-level categorical variable and writing score, write, a continuous variable.
(Research Question): When high school students choose the program (general, vocational, and academic programs), how do their math and science scores and their social economic status (SES) affect their decision?
prog
ses general academic vocation
low 16 19 12
middle 20 44 31
high 9 42 7# Since we are going to use Academic as the reference group, we need relevel the group.
hsb$prog2 <- relevel(as.factor(hsb$prog), ref = 2)
hsb$ses <- as.factor(hsb$ses)
levels(hsb$prog2)[1] "academic" "general" "vocation"# Run a multinomial model
multi_mo <- multinom(prog2 ~ ses + math + science + math*science, data = hsb,model=TRUE)# weights: 21 (12 variable)
initial value 219.722458
iter 10 value 173.831002
iter 20 value 167.382760
final value 166.951813
convergedCall:
multinom(formula = prog2 ~ ses + math + science + math * science,
data = hsb, model = TRUE)
Coefficients:
(Intercept) sesmiddle seshigh math science math:science
general 5.897618 -0.4081497 -1.1254491 -0.1852220 0.01323626 0.001025283
vocation 22.728283 0.8402168 -0.5605656 -0.5036705 -0.28297703 0.006185571
Std. Errors:
(Intercept) sesmiddle seshigh math science math:science
general 0.002304064 0.2613732 0.2134308 0.02694593 0.02953364 0.0004761369
vocation 0.003856861 0.2959741 0.1984775 0.02681947 0.03142872 0.0004760567
Residual Deviance: 333.9036
AIC: 357.9036 Main effects
Analysis of Deviance Table (Type II tests)
Response: prog2
LR Chisq Df Pr(>Chisq)
ses 12.922 4 0.01166 *
math 39.156 2 0.000000003143 ***
science 8.134 2 0.01713 *
math:science 5.249 2 0.07247 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 CoxSnell Nagelkerke
0.3102655 0.3565873 # A tibble: 12 × 8
y.level term estimate std.error statistic p.value conf.low conf.high
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 general (Intercept) 3.64e+2 0.00230 2560. 0 3.63e+2 3.66e+2
2 general sesmiddle 6.65e-1 0.261 -1.56 1.18e- 1 3.98e-1 1.11e+0
3 general seshigh 3.25e-1 0.213 -5.27 1.34e- 7 2.14e-1 4.93e-1
4 general math 8.31e-1 0.0269 -6.87 6.25e-12 7.88e-1 8.76e-1
5 general science 1.01e+0 0.0295 0.448 6.54e- 1 9.56e-1 1.07e+0
6 general math:science 1.00e+0 0.000476 2.15 3.13e- 2 1.00e+0 1.00e+0
7 vocation (Intercept) 7.43e+9 0.00386 5893. 0 7.37e+9 7.48e+9
8 vocation sesmiddle 2.32e+0 0.296 2.84 4.53e- 3 1.30e+0 4.14e+0
9 vocation seshigh 5.71e-1 0.198 -2.82 4.74e- 3 3.87e-1 8.42e-1
10 vocation math 6.04e-1 0.0268 -18.8 1.10e-78 5.73e-1 6.37e-1
11 vocation science 7.54e-1 0.0314 -9.00 2.18e-19 7.09e-1 8.01e-1
12 vocation math:science 1.01e+0 0.000476 13.0 1.33e-38 1.01e+0 1.01e+0Another way to understand the model using the predicted probabilities is to look at the averaged predicted probabilities for different values of the continuous predictor variable math within each level of ses.
# Extract coefficients
coef_df <- as.data.frame(coef(multi_mo))
coef_df$Term <- row.names(coef_df)
# Melt the dataframe for ggplot
library(reshape2)
melted_coef_df <- melt(coef_df, id.vars = c("Term", "(Intercept)"))
# Plot using ggplot2
library(ggplot2)
ggplot(melted_coef_df, aes(x = Term, y = value, fill = variable)) +
geom_bar(stat = "identity", position = position_dodge()) +
theme_minimal() +
labs(x = "Term", y = "Coefficient", fill = "Outcome") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
8.2.0.1 Write-up
(Research Question): When high school students choose the program (general, vocational, and academic programs), how do their math and science scores and their social economic status (SES) affect their decision?
A one-unit increase in math is associated with the decrease in the log odds of being in general program vs. academic program in the amount of .19 (one-unit increase in the variable math is .83 for being in general program vs. academic program).
Students in the highest social status level (SES = 3), compared to the lowest (SES = 1), are less likely to be in the general program compared to the academic one. The chance decreases by about 1.125 times, b = -1.125, Wald χ2(1) = -5.27, p <.001. This means their odds are about 0.325 times lower, making students from lower social status more inclined to pick the general program over the academic one.
Similarly, for high SES students (compared to low), the likelihood of being in the vocational program instead of the academic program drops by 0.56 times, b = -0.56, Wald χ2(1) = -2.82, p < 0.01. In other words, lower-status students (compared to high SES) prefer the vocational program over the academic one.
8.3 Poisson regression
Here, we’re looking at whether prog and math predict number of awards
p <- read.csv("https://stats.idre.ucla.edu/stat/data/poisson_sim.csv")
p <- within(p, {
prog <- factor(prog, levels=1:3, labels=c("General", "Academic",
"Vocational"))
id <- factor(id)
})
summary(p) id num_awards prog math
1 : 1 Min. :0.00 General : 45 Min. :33.00
2 : 1 1st Qu.:0.00 Academic :105 1st Qu.:45.00
3 : 1 Median :0.00 Vocational: 50 Median :52.00
4 : 1 Mean :0.63 Mean :52.65
5 : 1 3rd Qu.:1.00 3rd Qu.:59.00
6 : 1 Max. :6.00 Max. :75.00
(Other):194 ggplot(p, aes(num_awards, fill = prog)) +
geom_histogram(binwidth=.5, position="dodge") + theme_classic()
Call:
glm(formula = num_awards ~ prog + math, family = "poisson", data = p)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.2043 -0.8436 -0.5106 0.2558 2.6796
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.24712 0.65845 -7.969 0.0000000000000016 ***
progAcademic 1.08386 0.35825 3.025 0.00248 **
progVocational 0.36981 0.44107 0.838 0.40179
math 0.07015 0.01060 6.619 0.0000000000362501 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 287.67 on 199 degrees of freedom
Residual deviance: 189.45 on 196 degrees of freedom
AIC: 373.5
Number of Fisher Scoring iterations: 6Cameron and Trivedi (2009) recommended using robust standard errors for the parameter estimates to control for mild violation of the distribution assumption that the variance equals the mean.
cov.m1 <- vcovHC(m1, type="HC0")
std.err <- sqrt(diag(cov.m1))
r.est <- cbind(Estimate= coef(m1), "Robust SE" = std.err,
"Pr(>|z|)" = 2 * pnorm(abs(coef(m1)/std.err), lower.tail=FALSE),
LL = coef(m1) - 1.96 * std.err,
UL = coef(m1) + 1.96 * std.err)
r.est Estimate Robust SE Pr(>|z|) LL UL
(Intercept) -5.2471244 0.64599839 0.000000000000000456663 -6.51328124 -3.98096756
progAcademic 1.0838591 0.32104816 0.000735474482416738676 0.45460476 1.71311353
progVocational 0.3698092 0.40041731 0.355715684208826043999 -0.41500870 1.15462716
math 0.0701524 0.01043516 0.000000000017839751696 0.04969947 0.090605328.3.0.1 Plot predictions
## calculate and store predicted values
p$phat <- predict(m1, type="response")
## order by program and then by math
p <- p[with(p, order(prog, math)), ]
## create the plot
ggplot(p, aes(x = math, y = phat, colour = prog)) +
geom_point(aes(y = num_awards), alpha=.5, position=position_jitter(h=.2)) +
geom_line(size = 1) + theme_classic() +
labs(x = "Math Score", y = "Expected number of awards")
8.3.0.2 Write up
Being in an academic program was associated with a significant increase in the number of awards, b = 1.084, SE = 0.358, z = 3.025, p = 0.00248, indicating that students in academic programs tend to receive more awards than those in general programs, holding math scores constant.
Being in a vocational program did not significantly predict the number of awards compared to being in a general program, b = 0.370, SE = 0.441, z = 0.838, p = 0.40179, suggesting no significant difference in the expected count of awards between vocational and general program students, again holding math scores constant.
Math scores were also a significant predictor of the number of awards, b = 0.07015, SE = 0.01060, z = 6.619, p < 0.0001, suggesting that, regardless of program type, an increase in math scores is associated with an increase in the expected number of awards.
8.4 Ordinal regression
library(MASS) # For ordinal logistic regression (polr)
# Generate example data
set.seed(123)
data <- data.frame(
StudyHours = rnorm(100, mean = 5, sd = 2), # Simulating study hours
Performance = ordered(sample(1:5, 100, replace = TRUE), levels = c(1, 2, 3, 4, 5), labels = c("Poor", "Below Average", "Average", "Above Average", "Excellent"))
)
# Fit an ordinal logistic regression model
model <- polr(Performance ~ StudyHours, data = data)
summary(model)Call:
polr(formula = Performance ~ StudyHours, data = data)
Coefficients:
Value Std. Error t value
StudyHours 0.1162 0.09861 1.178
Intercepts:
Value Std. Error t value
Poor|Below Average -0.5097 0.5491 -0.9284
Below Average|Average 0.4270 0.5379 0.7938
Average|Above Average 0.9074 0.5377 1.6876
Above Average|Excellent 1.5883 0.5552 2.8607
Residual Deviance: 311.9673
AIC: 321.9673 8.4.0.1 Get p-values
Value Std. Error t value
StudyHours 0.1161846 0.09860927 1.1782316
Poor|Below Average -0.5097395 0.54906589 -0.9283759
Below Average|Average 0.4269730 0.53789874 0.7937795
Average|Above Average 0.9073994 0.53768046 1.6876183
Above Average|Excellent 1.5882928 0.55521379 2.8606868## calculate and store p values
p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2
## combined table
(ctable <- cbind(ctable, "p value" = p)) Value Std. Error t value p value
StudyHours 0.1161846 0.09860927 1.1782316 0.238704296
Poor|Below Average -0.5097395 0.54906589 -0.9283759 0.353212615
Below Average|Average 0.4269730 0.53789874 0.7937795 0.427323829
Average|Above Average 0.9073994 0.53768046 1.6876183 0.091484520
Above Average|Excellent 1.5882928 0.55521379 2.8606868 0.004227244The significance of “Above Average|Excellent” suggests that study hours become more influential in determining whether students achieve Above Average vs Excellent.
8.4.0.2 Plot ordinal
# Create a sequence of study hours for prediction
new_data <- data.frame(StudyHours = seq(min(data$StudyHours), max(data$StudyHours), length.out = 100))
# Predict probabilities for each performance category
predicted_probs <- as.data.frame(predict(model, newdata = new_data, type = "probs"))
# Rename the columns for clarity
colnames(predicted_probs) <- c("Poor", "Below Average", "Average", "Above Average", "Excellent")
# Create a visualization
ggplot(predicted_probs, aes(x = new_data$StudyHours)) +
geom_line(aes(y = `Poor`, color = "Poor"), size = 1) +
geom_line(aes(y = `Below Average`, color = "Below Average"), size = 1) +
geom_line(aes(y = `Average`, color = "Average"), size = 1) +
geom_line(aes(y = `Above Average`, color = "Above Average"), size = 1) +
geom_line(aes(y = `Excellent`, color = "Excellent"), size = 1) +
labs(title = "Ordinal Logistic Regression: Predicting Student Performance",
x = "Study Hours",
y = "Predicted Probability") +
scale_color_manual(values = c("Poor" = "#1f77b4",
"Below Average" = "#ff7f0e",
"Average" = "#2ca02c",
"Above Average" = "#d62728",
"Excellent" = "#9467bd"),
name = "Performance Level",
limits = c("Excellent","Above Average", "Average", "Below Average", "Poor")) + # Explicitly set the order
theme_minimal()
---
title: 'Robust Regression, Moderation, Mediation, and Nonlinear Regression'
author: "Kareena del Rosario"
date: "`r Sys.Date()`"
output: 
  html_document:
    theme: simplex
    highlight: haddock
    toc: true
    code_download: true
    number_sections: true
    toc_float: 
      collapsed: false
editor_options: 
  markdown: 
    wrap: 72
---

```{=html}
<style type="text/css">


h1.title {
  color: DarkRed;
}
h1 { /* Header 1 */
  color: DarkRed;
}
h2 { /* Header 2 */
  color: DarkRed;
}
h3 { /* Header 3 */
  color: DarkRed;

</style>
```
```{r, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, 
                      comment = NA,
                      warning = FALSE,
                      message = FALSE,
                      tidy = 'styler',
                      error = FALSE, 
                      highlight = TRUE, 
                      prompt = FALSE,
                      R.options = list(width = 90))
options(scipen = 999)

print_p <- function(p) {
  print(round(p, 4), quote = FALSE)
}
```

**To see a summary of the regression assumptions and more ways run test
diagnostics, see our previous
[lab](https://rpubs.com/kareena_delrosario/lab7_linear_regression2024)**

```{r message=FALSE, warning=FALSE, results='hide'}

pkgs <- c("tidyverse", 
          "dplyr", 
          "haven", 
          "foreign", 
          "lme4", 
          "nlme", 
          "lsr", 
          "emmeans", 
          "afex", 
          "knitr", 
          "kableExtra", 
          "car",
          "mediation",
          "rockchalk",
          "multilevel",
          "bda",
          "gvlma",
          "stargazer",
          "QuantPsyc",
          "pequod",
          "MASS",
          "texreg",
          "pwr",
          "effectsize",
          "semPlot",
          "lmtest",
          "semptools",
          "conflicted",
          "nnet",
          "ordinal",
          "DescTools")


packages <- rownames(installed.packages())
p_to_install <- pkgs[!(pkgs %in% packages)]

if(length(p_to_install) > 0){
  install.packages(p_to_install)
}

lapply(pkgs, library, character.only = TRUE)

# devtools::install_github("cardiomoon/semMediation")
library(semMediation)

# tell R which package to use for functions that are in multiple packages
these_functions <- c("mutate", "select", "summarize", "filter")
lapply(these_functions, conflict_prefer, "dplyr")

conflict_prefer("mutate", "dplyr")
conflict_prefer("select", "dplyr")
conflict_prefer("summarize", "dplyr")



```

# Quick check-in on homework 2

### Power analysis for ANOVA and chi-square

#### ANOVA

```{r}
# quick ANOVA for demonstration
# create id variable for error term
iris_afex <- iris %>% 
  dplyr::mutate(id = row_number())

anova_ex <- afex::aov_car(Sepal.Length ~ Species + Error(id), data = iris_afex)
summary(anova_ex)


# convert eta-squared to cohen's F with this function:
library(effectsize)
cohens_f(anova_ex)
```

#### Chi-square

```{r}
# here is another power analysis function that allows you to use cohen's w.
library(pwr)
pwr.chisq.test(w=0.2,df=1,power=.95,sig.level=0.05)
```

#### Regression

```{r, message=FALSE, warning=FALSE}
library(effectsize)

# Get f-squared
reg_ex <- lm(Sepal.Length ~ Species, data = iris_afex)
cohens_f_squared(reg_ex)

# Manually calculate f-squared
r_squared <- summary(reg_ex)$r.squared
f_squared <- r_squared / (1 - r_squared)

library(pwr)
power_analysis <- pwr.f2.test(u = 2, f2 = .15, sig.level = 0.05, power = 0.95)
print(power_analysis)
```

### Planned contrasts vs pairwise comparisons

Gender (Male, Female) Film (Bridget Jones, Memento)

*For people who watched Memento, do women report higher arousal after
watching the film than men?*

#### Planned contrasts

```{r}
d.data <- read.delim("/Users/kareenadelrosario/Downloads/ChickFlick.dat")

d.data <- d.data %>% 
  mutate(gender = as.factor(ifelse(gender == "Female", 0, 1)),
         film = as.factor(ifelse(film == "Memento", 0, 1)))

contrasts(d.data$gender) = contr.treatment(2, base = 2) # female = 1, male = 0
contrasts(d.data$film) # memento = 0, bridget jones = 1
```

```{r}
d_model <- lm(arousal ~ gender * film, data = d.data)
summary(d_model)
```

#### Pairwise comparisons

```{r}
d_emm <- emmeans(d_model, specs = c("gender", "film"))
pairs(d_emm)
```

#### Why can't I just filter out Bridget Jones?

```{r}
d.data.f <- d.data %>% 
  filter(film == 0)

f_model <- lm(arousal ~ gender, data = d.data.f)
summary(f_model)
```

------------------------------------------------------------------------

# Robust Regression

*credit: <https://stats.oarc.ucla.edu/r/dae/robust-regression/>*

**What is the difference between OLS and robust regression? When would
you use one over the other?**

------------------------------------------------------------------------

## Dealing with outliers using Hubert and bisquare weights

Robust regression is suitable for cases where you'd typically use OLS
regression but encounter *outliers or high leverage points that aren't
errors or from a different population*. Instead of excluding these
points or treating all data equally as in OLS regression, robust
regression offers a middle ground by assigning different weights to
observations based on their reliability. Essentially, it's a weighted
least squares approach that adjusts weights in response to the features
of the data.

Terms to know:

```         
- Residual: The difference between the predicted value (based on the regression equation) and the actual, observed value.

- Outlier: In linear regression, an outlier is an observation with large residual. In other words, it is an observation whose dependent-variable value is unusual given its value on the predictor variables. An outlier may indicate a sample peculiarity or may indicate a data entry error or other problem.

- Leverage: An observation with an extreme value on a predictor variable is a point with high leverage. Leverage is a measure of how far an independent variable deviates from its mean. High leverage points can have a great amount of effect on the estimate of regression coefficients.

- Influence: An observation is said to be influential if removing the observation substantially changes the estimate of the regression coefficients. Influence can be thought of as the product of leverage and outlierness.

- Cook’s distance (or Cook’s D): A measure that combines the information of leverage and residual of the observation.
```

```{r}
cdata <- read.dta("https://stats.idre.ucla.edu/stat/data/crime.dta")

head(cdata)
```

#### Variables

-   (sid) State ID
-   (state) State name
-   (crime) Violent crimes per 100,000 people
-   (poverty) Percent of population living under poverty line
-   (single) Percent of population that are single parents
    -   Total observations: 51
    -   crime \~ poverty + single

#### Run OLS

We will begin by running an OLS regression and looking at diagnostic
plots examining residuals, fitted values, Cook’s distance, and leverage.

```{r}
summary(ols <- lm(crime ~ poverty + single, data = cdata))
```

### Identify outliers

```{r}
plot(ols)

```

From these plots, we can identify observations 9, 25, and 51 as possibly
problematic to our model. We can look at these observations to see which
states they represent.

```{r}
cdata[c(9, 25, 51), 1:2]
```

DC, Florida and Mississippi have either high leverage or large
residuals. We can display the observations that have relatively large
values of Cook’s D. A conventional cut-off point is 4/n, where n is the
number of observations in the data set.

```{r}
d1 <- cooks.distance(ols) # captures influential observations
r <- stdres(ols) # computes standardized residuals
a <- cbind(cdata, d1, r) 
a[d1 > 4/51, ] # Filters the combined data frame a to display only those observations for which Cook's distance is greater than 4/n. n = 51 
```

Now we will look at the residuals. We will generate a new variable
called absr1, which is the absolute value of the residuals (because the
sign of the residual doesn’t matter). We then print the ten observations
with the highest absolute residual values.

```{r}
rabs <- abs(r)
a <- cbind(cdata, d1, r, rabs)
asorted <- a[order(-rabs), ]
asorted[1:10, ]
```

### IRLS with Huber weights

Now let’s run our first robust regression. Robust regression is done by
iterated re-weighted least squares (IRLS). The command for running
robust regression is **rlm** in the **MASS** package. There are several
weighting functions that can be used for IRLS. We are going to first use
the Huber weights in this example. We will then look at the final
weights created by the IRLS process. This can be very useful.

```{r}
summary(rr.huber <- rlm(crime ~ poverty + single, data = cdata))
```

Let's take a look at the weights of the top 15 largest residuals

```{r}
hweights <- data.frame(state = cdata$state, resid = rr.huber$resid, weight = rr.huber$w)
hweights2 <- hweights[order(rr.huber$w), ]
hweights2[1:15, ]
```

We can see that roughly, as the absolute residual goes down, the weight
goes up.

All observations not shown above have a weight of 1. In OLS regression,
all cases have a weight of 1. Hence, the more cases in the robust
regression that have a weight close to one, the closer the results of
the OLS and robust regressions.

### IRLS with bisquare weights

Next, let’s run the same model, but using the bisquare weighting
function. Again, we can look at the weights.

```{r}
rr.bisquare <- rlm(crime ~ poverty + single, data=cdata, psi = psi.bisquare)
summary(rr.bisquare)

# if you need significance values. MASS doesn't trust p-values and won't report them.
# texreg(rr.bisquare, ci.force=TRUE)
```

Here are the weights for the same 15 observations using bisquare weights

```{r}
biweights <- data.frame(state = cdata$state, resid = rr.bisquare$resid, weight = rr.bisquare$w)
biweights2 <- biweights[order(rr.bisquare$w), ]
biweights2[1:15, ]
```

We can see that the weight given to Mississippi is dramatically lower
using the bisquare weighting function than the Huber weighting function
and the parameter estimates from these two different weighting methods
differ.

**When comparing the results of a regular OLS regression and a robust
regression, if the results are very different, you will most likely want
to use the results from the robust regression.** Large differences
suggest that the model parameters are being highly influenced by
outliers. Different functions have advantages and drawbacks. Huber
weights can have difficulties with severe outliers, and bisquare weights
can have difficulties converging.

------------------------------------------------------------------------

## GLS for heteroscedasticity

Robust regression does not directly address heteroscedasticity. To
account for heteroscedasticity or autocorrelation in GLS, you would
typically need to specify a particular structure for the covariance
matrix of the errors that reflects the nature of the heteroscedasticity
or correlation you're dealing with. In other words, what is driving the
difference in variance?

![Heteroskedasticity.](heteroskedasticity.webp)

Check the residuals vs fitted plot to see if the line is curved. That
would indicate heteroscedasticity

```{r}
res <- residuals(ols)
yhat <- fitted(ols)
plot(cdata$poverty,res, xlab="poverty", ylab="residuals")
plot(cdata$single,res, xlab="single", ylab="residuals")
```

### Breush Pagan Test

```{r}
# why might this be significant?
bptest(ols)
```

```{r}
ggplot(cdata, aes(x = single, y = crime)) +
  geom_point(aes(color = poverty), alpha = 0.5) +  # Color points by poverty level
  geom_smooth(method = "lm", formula = y ~ x, se = FALSE, color = "green") +
  labs(x = "Single Parent Percentage", y = "Crime Rate",
       title = "Crime Rate vs. Single Parent Percentage",
       subtitle = "Colored by Poverty Level") +
  theme_minimal()
```

#### Using weights in the GLS Model

```{r}
# Let's say we find that as single-parent household % increases, crime variance increases. This suggests a proportional relationship between single-parent and crime, so we'll account for variance changes as a power function 
glsModel <- gls(crime ~ poverty + single, data = cdata, 
               weights = varPower(form = ~ single))
summary(glsModel)

# Plotting standardized residuals vs fitted values
plot(fitted(glsModel), residuals(glsModel, type = "normalized"),
     xlab = "Fitted values", ylab = "Standardized Residuals")
abline(h = 0, lty = 2)
```

```{r}
# Let's say that the variability in crime scores differs as a function of the state (could formally test with levene's test). We could account for that on the weights line. Note this doesn't work here because each state only has one entry.
glsModel2 <- gls(crime ~ poverty + single, data = cdata, 
               weights = varIdent(form = ~ 1 | state))

summary(glsModel2)
```

## Generating robust CIs with bootstrapping

Bootstrapping can be helpful if you have a small sample or your data
violate the regression assumptions and you want to get more accurate CI
estimates. While this won't correct for heterogeneity of variance,
bootstrapping can be used to estimate robust standard errors for
regression coefficients.

When to use bootstrapping:

-   Assumptions are violated
-   Sample size is small
-   Presence of outliers

```{r}
bootReg <- function(formula, data, indices) {
  d <- data[indices, ]  # Use 'indices' to create a subset dataframe 'd'
  fit <- lm(formula, data = d)
  return(coef(fit))
}

bootResults <- boot (statistic = bootReg, formula = crime ~ poverty + single, data = cdata, R = 2000)

# based on the bootstrapping, how biased are our estimates?
summary(bootResults)
```

```{r}
summary(ols)
# intercept (index = 1)
boot.ci(bootResults, type = "bca", index = 1) # bca = bias corrected and accelerated
```

```{r}
# poverty (index = 2)
boot.ci(bootResults, type = "bca", index = 2) 
```

```{r}
# single (index = 3)
boot.ci(bootResults, type = "bca", index = 3) 
```

How do these compare to the OLS confidence intervals?

```{r}
confint(ols)
```

------------------------------------------------------------------------

## Your turn!

A study was carried out to explore the relationship between Aggression
and several potential predicting factors in 666 children who had an
older sibling.

Variables measured were:

-   Parenting_Style (high score = bad parenting practices)
-   Computer\_ Games (high score = more time spent playing computer
    games)
-   Television (high score = more time spent watching television)
-   Diet (high score = the child has a good diet low in additives)
-   Sibling_Aggression (high score = more aggression seen in their older
    sibling).

*The data are in the file ChildAggression.dat.*

1.  Run a multiple regression testing the effect of these variables,
    using "Aggression" as the DV.
2.  Obtain the standardized parameter estimates (aka standardized
    betas).
3.  Check whether the model meets the regression assumptions using both
    plots and formal tests: a. homoscedasticity b. multicollinearity c.
    independence (no autocorrelation in residuals)
4.  Report your results -- how would you interpret the R-squared? Which
    variables significantly predicted aggression?

```{r}
df <- read_delim("/Users/kareenadelrosario/Downloads/ChildAggression.dat", delim = " ")
```

```{r}
model <- lm(Aggression ~ Television + Computer_Games + Sibling_Aggression + Diet + Parenting_Style, data = df)

summary(model)
```

```{r}
lm.beta(model)
```

**Residuals vs Fitted:** is used to check the assumptions of linearity.
If the residuals are spread equally around a horizontal line without
distinct patterns (red line is approximately horizontal at zero), that
is a good indication of having a linear relationship.

**Normal Q-Q:** is used to check the normality of residuals assumption.
If the majority of the residuals follow the straight dashed line, then
the assumption is fulfilled.

**Scale-Location:** is used to check the homoscedasticity of residuals
(equal variance of residuals). If the residuals are spread randomly and
the see a horizontal line with equally (randomly) spread points, then
the assumption is fulfilled.

**Residuals vs Leverage:** is used to identify any influential value in
our dataset. Influential values are extreme values that might influence
the regression results when included or excluded from the analysis. Look
for cases outside of a dashed line (if there is a concerning point,
you'll see red lines pop up).

Homoscedasticity: residuals vs fitted & bp

```{r}
plot(model)
```

```{r}
bptest(model)
```

Multicollinearity

-   If the largest VIF is greater 10, then there's cause for concern
-   If the average VIF is substantially greater than 1, the model may be
    biased
-   Tolerance below 0.1 means there's a serious problem
-   Tolerance below 0.2 means there's a potential problem

```{r}
# vif
vif(model)

# average vif
mean(vif(model))

# tolerance
1/vif(model)
```

Independence

```{r}
durbinWatsonTest(model)
```

Skew

```{r}
gvlma(model)
```

------------------------------------------------------------------------

# Centering, rescaling, standardizing, contrast coding your predictors

*adapted from:
<https://advstats.psychstat.org/book/mregression/index.php>*

Note that you never HAVE to center/recode your predictors. It should
**never** influence the test significance-- just the interpretation of
your intercept and coefficients.

-   If you have *continuous predictors*, you can **center**.
-   If you have *categorical predictors*, you can **dummy code** or
    **effects code** (see ANOVA labs for info).
-   If you have *predictors with different scales*, you can **standardize**.

Let's say we're interested in the effects of high school GPA (h.gpa),
SAT, and quality of recommendation letters (recommd) on college GPA
(c.gpa).

```{r, message=FALSE}
gpa_df <- read.csv("/Users/kareenadelrosario/Downloads/gpa.csv")

head(gpa_df)
```

```{r}
par(mfrow=c(2,2))
plot(gpa_df$h.gpa, gpa_df$c.gpa)
plot(gpa_df$SAT, gpa_df$c.gpa)
plot(gpa_df$recommd, gpa_df$c.gpa)


# original model
gpaModel<- lm(c.gpa ~ h.gpa + SAT + recommd, data = gpa_df)

summary(gpaModel)
```

How would you interpret these estimates?

#### Centering

```{r}
# center separately
gpa_df$h.gpaC <- scale(gpa_df$h.gpa, center=TRUE, scale=FALSE) # mean center without rescaling 

# shortcut
centeredModel<- lm(c.gpa~ h.gpaC + scale(SAT,scale=F) + scale(recommd,scale=F), data=gpa_df) 

summary(centeredModel)
```

#### Standardizing

When predictors like GPA (typically on a 0 to 4 scale) and SAT scores
(typically on a 400 to 1600 scale) are involved, their coefficients can
be difficult to compare directly because a one-unit change means
something very different for each predictor. Through standardization,
however, we can *remove the scales of the predictors* and therefore make
the coefficients relatively more comparable. We can standardize
predictors only or both predictors and the outcome variable.

After standardization, the variable means are all 0 and variances are
all 1. The beta coefficient (output), tells us how many standard
deviations the predicted DV changes given one standard deviation change
in the IV when the other IVs are held constant.

In R, scale() can also be used for standardization. Note that to skip
the estimation of the intercept, one can add -1 in the regression model
formular.

```{r}
# same as above except we remove the scale = F statement
betaModel<-lm(scale(c.gpa) ~ scale(h.gpa) + scale(SAT) + scale(recommd)-1, data=gpa_df)

summary(betaModel)
```

Alternatively, you could feed your centered model through lm.beta() to
get the betas without rerunning the model

```{r}
lm.beta(centeredModel)
```

------------------------------------------------------------------------

# Moderation vs Mediation

*moderation & mediation content was adapted from:
<https://ademos.people.uic.edu/Chapter14.html#>*

You can think of this distinction as mediation answers **how** two
variables are related whereas moderation tells us **it depends**.

-   Mediation analysis tests for a hypothetical causal relationship in
    which X -\> Y, and the underlying mechanism can be explained by M.
-   Moderation looks at the influence of Z on X-\>Y to test for when or
    under what conditions an effect occurs. Moderators can strengthen,
    weaken, or reverse the nature of a relationship.

Mediators describe the how or why of a (typically well-established)
relationship between two other variables and are sometimes called
intermediary variables since they often describe the process through
which an effect occurs. This is also sometimes called an indirect
effect. For instance, people with higher incomes tend to live longer but
this effect is explained by the mediating influence of having access to
better health care.

# Moderation Analyses

Moderation tests whether a variable (Z) affects the direction and/or
strength of the relation between an IV (X) and a DV (Y). In other words,
moderation tests for interactions that affect WHEN relationships between
variables occur. Moderators are conceptually different from mediators
(when versus how/why) but some variables may be a moderator or a
mediator depending on your question.

Like mediation, moderation assumes that there is little to no
measurement error in the moderator variable and that the DV did not
CAUSE the moderator.

![Basic Moderation Model.](moderation_model.jpeg)

## Example Moderation Data

In this example we'll say we are interested in whether the relationship
between the **number of hours of sleep (X)** a graduate student receives
and the **attention that they pay to this tutorial (Y)** is influenced
by their **consumption of coffee (Z)**.

Here we create the moderation effect by making our DV (Y) the product of
levels of the IV (X) and our moderator (Z).

```{r, message=FALSE}

set.seed(123)#Standardizes the numbers generated by rnorm

N  <- 100 #Number of participants; graduate students
X.hours  <- abs(rnorm(N, 6, 4)) #IV; Hours of sleep
X1 <- abs(rnorm(N, 60, 30)) #Adding some systematic variance for our DV
Z.coffee  <- rnorm(N, 30, 8) #Moderator; Ounces of coffee consumed
Y.attn  <- abs((-0.8*X.hours) * (0.2*Z.coffee) - 0.5*X.hours - 0.4*X1 + 10 + rnorm(N, 0, 3)) #DV; Attention Paid
Moddata <- data.frame(X.hours, X1, Z.coffee, Y.attn)

summary(Moddata)
```

Moderation can be tested by looking for significant interactions between
the moderating variable (Z) and the IV (X). **It is important to mean
center both your moderator and your IV to reduce multicollinearity and
make interpretation easier.** Centering can be done using the *scale*
function, which subtracts the mean of a variable from each value in that
variable.

```{r}
#Moderation 
fitMod <- lm(Y.attn ~ X.hours + Z.coffee + X.hours:Z.coffee, data = Moddata) #Model interacts IV & moderator

# Alternative formatting
# fitMod <- lm(Y.wake ~ X.hours*Z.coffee) 


print_p(coef(summary(fitMod)))
```

### How would you interpret the coefficients and intercept?

------------------------------------------------------------------------

## Centering predictors

Sometimes our coefficients don't make any sense. We can make the 0
meaningful by centering our predictors.

```{r, message=FALSE}
### Two ways to center
Moddata <- Moddata %>% 
  mutate(X.hoursC = X.hours - mean(X.hours),
         Z.coffeeC = Z.coffee - mean(Z.coffee))

# Centering Data
X.hoursC    <- scale(X.hours, center=TRUE, scale=FALSE) #Centering IV; hours of sleep
Z.coffeeC    <- scale(Z.coffee,  center=TRUE, scale=FALSE) #Centering moderator; coffee consumption


##################################

# Reanalyze with centered variables
fitModC <- lm(Y.attn ~ X.hoursC + Z.coffeeC + X.hoursC:Z.coffeeC, data = Moddata) 
print_p(coef(summary(fitModC)))
```

------------------------------------------------------------------------

```{r}
gvlma(fitModC) #data is positively skewed; could log transform 
```

```{r, results = 'asis'}

#Data Summary
stargazer(fitModC, type="html", digits = 2, font.size = "footnotesize", title = "Sleep and Coffee on Attention")

#Plotting
ps  <- plotSlopes(fitModC, plotx="X.hoursC", modx="Z.coffeeC", xlab = "Sleep", ylab = "Attention Paid", modxVals = "std.dev")
```

## Interpreting Moderation Results

Our model shows a significant interaction between hours slept and coffee
consumption on attention paid to this tutorial (b = .23, SE = .04, *p*
\< .001). However, we'll need to unpack this interaction visually to get
a better idea of what this means.

The *rockchalk* function will automatically plot the simple slopes (1 SD
above and 1 SD below the mean) of the moderating effect. 

  * This figure shows that those who drank less coffee (the black line) paid more
attention with the more sleep that they got last night but paid less
attention overall that average (the blue line). 
  * Those who drank more coffee (the green line) paid more attention when they slept more as well and paid more attention than average. 
  * The difference in the slopes for those who drank more or less coffee shows that coffee consumption moderates the relationship between hours of sleep and attention paid.

## Decomposing interactions

*credit: <https://stats.oarc.ucla.edu/r/seminars/interactions-r/#s2>*

You know that hours spent exercising improves weight loss, but how does
it interact with effort? 

This is a hypothetical study of weight loss for 900 participants in a
year-long study of 3 different exercise programs, a jogging program, a
swimming program, and a reading program which serves as a control
activity. Variables include

-   **loss:** weight loss (continuous), positive = weight loss, negative
    scores = weight gain
-   **hours:** hours spent exercising (continuous)
-   **effort:** effort during exercise (continuous), 0 = minimal physical
    effort and 50 = maximum effort
-   **gender:** participant gender (binary)
    -   male=1
    -   female=2

```{r}
dat <- read.csv("https://stats.idre.ucla.edu/wp-content/uploads/2019/03/exercise.csv")

dat$gender <- factor(dat$gender,labels=c("male","female"))
```


### Continuous by continuous

**How do we interpret an interaction with continuous predictors? And
what is extrapolating?**

$Weight\ Loss = b_0 + b_1Hours + b_2Effort + b_3Hours*Effort$

```{r}
contcont <- lm(loss~hours*effort,data=dat)
summary(contcont)
```

Although we may think that the slope of Hours should be positive at
levels of Effort, remember that in this case, Effort is zero. As we see
in our data, this is improbable as the minimum value of effort is 12.95.

```{r}
summary(dat$effort)
```

What would we expect weight loss to look like at average effort?

```{r}
(mylist <- list(hours=2,effort=30))
emmeans(contcont, ~ hours*effort, at=mylist)
```

The results show that predicted weight loss is 10.2 pounds if we put in
two hours of exercise and an effort level of 30; this seems reasonable.
Let’s see what happens when we predict weight loss for two hours of
exercise given an effort level of 0.

```{r}
mylist <- list(hours=2,effort=0) 
emmeans(contcont, ~ hours*effort, at=mylist)
```

The predicted weight gain is now 11 pounds. Weird, right? This is an
example of **extrapolating**, which means we are making predictions
about our data beyond what the data can support. This is why we should
always choose reasonable values of our predictors in order to interpret
our data properly.

![extrapolating](extrapolating.png)

We know to choose reasonable values when predicting values. The same
concept applies when *decomposing an interaction.* Our output suggests
that Hours varies by levels of Effort. Since effort is continuous, we
can choose an infinite set of values with which to fix effort.

For ease of presentation, we can use what's called "spotlight analysis"
(Aiken & West, 1991). To do a spotlight analysis, we'll divide Effort
into three levels: low, average, high.

\$EffA = \overline{Effort} + \sigma(Effort) \$

\$Eff = \overline{Effort} \$

\$EffB = \overline{Effort} - \sigma(Effort) \$

```{r}
# high effort
effa <- mean(dat$effort) + sd(dat$effort)
(effar <- round(effa,1))

# average effort
eff <- mean(dat$effort)
(effr <- round(eff,1))

# low effort
effb <- mean(dat$effort) - sd(dat$effort)
(effbr <- round(effb,1))
```

Recall that our simple slope is the relationship of hours on weight loss
fixed a particular values of effort. In R, we can obtain simple slopes
using the function *emtrends.* We first create a list which incorporates
the three values of effort we found above in preparation for spotlight
analysis.

```{r}
mylist <- list(effort=c(effbr,effr,effar))

emtrends(contcont, pairwise ~effort, var="hours",at=mylist, adjust="none")
```

All comparisons of simple slopes result in the same p-value as the
interaction itself.

Based on the tests above, yes the maginitude of the slope is larger
between “low” and “high” versus “medium” and “high”, but the two
p-values are the same.

```{r}
(mylist <- list(hours=seq(0,4,by=0.4),effort=c(effbr,effr,effar)))

emmip(contcont,effort~hours,at=mylist, CIs=TRUE)
```

**The results suggest that hours spent exercising is only effective for
weight loss if we put in more effort, which supports the rationale for
high intensity interval training.**

## Continuous by Categorical

The research question here is, do men and women (W) differ in the
relationship between Hours (X) and Weight loss? Here, we're going to use
dummy coding.

```{r}
dat$gender <- relevel(dat$gender, ref="female") 

contcat <- lm(loss~hours*gender,data=dat)
summary(contcat)
```

#### Obtaining simple slopes by each level of the categorical moderator

Since our goal is to obtain simple slopes of Hours by gender we use
emtrends. We do not use emmeans because this function gives us the
predicted values rather than slopes.

```{r}
emtrends(contcat, ~ gender, var="hours")
```

A common misconception is that since the simple slope of Hours is
significant for females but not males, we should have seen a significant
interaction. However, the interaction tests the difference of the Hours
slope for males and females and not whether each simple slope is
different from zero (which is what we have from the output above).

To test the difference in slopes, we add pairwise \~ gender to tell the
function that we want the pairwise difference in the simple slope of
Hours for females versus males.

```{r}
emtrends(contcat, pairwise ~ gender, var="hours")
```

Recall from our summary table, this is exactly the same as the
interaction, which verifies that we have in fact obtained the
interaction coefficient.

```{r}
(mylist <- list(hours=seq(0,4,by=0.4),gender=c("female","male")))
emmip(contcat, gender ~hours, at=mylist,CIs=TRUE)
```

Another common approach to plotting predicted values:

```{r}
newdata <- expand.grid(hours = seq(0, 4, by = 0.4), gender = c("female", "male"))
prediction <- predict(contcat, newdata, interval="confidence", level = 0.95)

# combine
newdata <- cbind(newdata, prediction)


ggplot(newdata, aes(x = hours, y = fit, color = gender)) +
  geom_line(size = 1) + 
  geom_point(size = 2, shape = 1, fill = "white") +
  geom_ribbon(aes(ymin = lwr, ymax = upr, fill = gender), alpha = 0.2, color = NA) +
  theme_minimal() +
  scale_color_manual(values = c("#4878D0", "#D65F5F")) +
  scale_fill_manual(values = c("#4878D0", "#D65F5F")) +
  labs(
    title = "Predicted Loss by Hours and Gender",
    x = "Hours",
    y = "Predicted Loss",
    color = "Gender",
    fill = "Gender"
  )

```

#### In sum

-   Predicted values are points on the graph.
-   Simple effects or slopes are the difference between two predicted
    values (i.e., two points).
-   Interactions are the difference between simple effects of slopes;
    -   for an interaction involving a continuous IV, it’s the
        difference of two slopes (i.e., two lines)
    -   for a categorical by categorical interaction, the interaction is
        the difference in the height of the bars in one group versus the
        difference of the heights in another group (a.k.a., difference
        of differences).

------------------------------------------------------------------------

# Mediation Analyses

The Baron & Kenny method is among the original methods for testing for
mediation but tends to have low statistical power. We're covering it
here because it provides a very clear approach to establishing
relationships between variables and is still occasionally requested by
reviewers. 

Mediation tests whether the effects of X (the independent variable) on Y
(the dependent variable) operate through a third variable, M (the
mediator). In this way, mediators explain the causal relationship
between two variables or "how" the relationship works.

![Basic Mediation Model.](mediation_model.png)

```         
c = the total effect of X on Y with no consideration of mediator variables
c'= the direct effect of X on Y after controlling for M 
ab= the indirect effect of X on Y through M

```

The above shows the standard mediation model. **Full mediation**
occurs when the effect of X on Y disappears with M in the model.
**Partial mediation** occurs when the effect of X on Y decreases by a
nontrivial amount (the actual amount is up for debate) with M in the
model.

### Example Mediation Data

In this example we'll say we are interested in whether the **number of
hours since dawn (X)** affect the **subjective ratings of wakefulness
(Y)** 100 graduate students through the **consumption of coffee (M).**

Note that we are intentionally creating a mediation effect here (because
statistics is always more fun if we have something to find) and we do so
below by creating M so that it is related to X and Y so that it is
related to M. This creates the causal chain for our analysis to parse.

```{r, message=FALSE}
#setwd("user location") #Working directory
set.seed(123) #Standardizes the numbers generated by rnorm; see Chapter 5
N <- 100 #Number of participants; graduate students
X.hours <- rnorm(N, 175, 7) #IV; hours since dawn
M.coffee <- 0.7*X.hours + rnorm(N, 0, 5) #Suspected mediator; coffee consumption 
Y.wake <- 0.4*M.coffee + rnorm(N, 0, 5) #DV; wakefulness
Meddata <- data.frame(X.hours, M.coffee, Y.wake)
```

## Method 1: Baron & Kenny

This is the original 4-step method used to describe a mediation effect.
Steps 1 and 2 use basic linear regression while steps 3 and 4 use
multiple regression.


Now, let's apply the Baron & Kenny method to our data:

The Steps:

1.  Estimate the relationship between X on Y (hours since dawn on degree
    of wakefulness)
    -   Path "c" must be significantly different from 0; must have a
        **total effect between the IV & DV**
    -   **Y \~ X = SIGNIFICANT**
2.  Estimate the relationship between X on M (hours since dawn on coffee
    consumption)
    -   Path "a" must be significantly different from 0; **IV and
        mediator must be related.**
    -   **M \~ X = SIGNIFICANT**
3.  Estimate the relationship between M on Y controlling for X (coffee
    consumption on wakefulness, controlling for hours since dawn)
    -   Path "b" must be significantly different from 0; **mediator and
        DV must be related.**
    -   **Y \~ M + X = SIGNIFICANT**
4.  Estimate the relationship between Y on X controlling for M
    (wakefulness on hours since dawn, controlling for coffee
    consumption)
    -   Should be **non-significant** and nearly 0.
    -   **X \~ Y + M = NON-SIGNIFICANT**

```{r, message=FALSE}
#1. Total Effect
fit <- lm(Y.wake ~ X.hours, data=Meddata)

#2. Path A (X on M)
fita <- lm(M.coffee ~ X.hours, data=Meddata)

#3. Path B (M on Y, controlling for X)
fitb <- lm(Y.wake ~ M.coffee + X.hours, data=Meddata)

#4. Reversed Path C (Y on X, controlling for M)
fitc <- lm(X.hours ~ Y.wake + M.coffee, data=Meddata)
```

```{r, message=FALSE, results='asis'}
#Summary Table
stargazer::stargazer(fit, fita, fitb, fitc, type="html", digits = 2, font.size = "footnotesize",title = "Baron and Kenny Method")

```

### Interpreting Baron & Kenny Results

-   Here we find that our total effect model shows a significant
    **positive relationship between hours since dawn (X) and wakefulness
    (Y)**.
-   Our Path A model shows that **hours since dawn (X) is also
    positively related to coffee consumption (M)**.
-   Our Path B model then shows that **coffee consumption (M) positively
    predicts wakefulness (Y) when controlling for hours since dawn
    (X)**.
-   Finally, **wakefulness (Y) does not predict hours since dawn (X)
    when controlling for coffee consumption (M)**.

Since the relationship between hours since dawn and wakefulness is no
longer significant when controlling for coffee consumption, this
suggests that coffee consumption does in fact mediate this relationship.
However, this method alone does not allow for a formal test of the
indirect effect so we don't know if the change in this relationship is
truly meaningful.

There are two primary methods for formally testing the significance of
the indirect test: the Sobel test & bootstrapping (covered under the
*mediation* method). These are considered outdated, so we're going to
move onto our preferred method.

## Method 2: The *Mediation* Package Method

This package uses the more recent bootstrapping method of Preacher &
Hayes (2004) to address the power limitations of the Sobel Test. This
method computes the point estimate of the indirect effect (ab) over a
large number of random sample (typically 1000) so it does not assume
that the data are normally distributed and is especially more suitable
for small sample sizes than the Baron & Kenny method.

To run the *mediate* function, we will again need a model of our IV
(hours since dawn), predicting our mediator (coffee consumption) like
our Path A model above. We will also need a model of the direct effect
of our IV (hours since dawn) on our DV (wakefulness), when controlling
for our mediator (coffee consumption). When can then use *mediate* to
repeatedly simulate a comparsion between these models and to test the
significance of the indirect effect of coffee consumption.

```{r, message=FALSE}

# Path A
fitM <- lm(M.coffee ~ X.hours,     data=Meddata) #IV on M; Hours since dawn predicting coffee consumption

# Total
fitY <- lm(Y.wake ~ X.hours + M.coffee, data=Meddata) #IV and M on DV; Hours since dawn and coffee predicting wakefulness

# Check skew
gvlma(fitM) #data is positively skewed; could log transform
gvlma(fitY)

fitMed <- mediate(fitM, fitY, treat="X.hours", mediator="M.coffee")
summary(fitMed)
plot(fitMed)
```

```{r}
#Bootstrap
fitMedBoot <- mediate(fitM, fitY, boot=TRUE, sims=2000, treat="X.hours", mediator="M.coffee")
summary(fitMedBoot)

plot(fitMedBoot)
```

### Interpreting *Mediation* Results

The *mediate* function gives us:

-   Average Causal Mediation Effects (ACME)
-   Average Direct Effects (ADE), our combined indirect and direct
    effects (Total Effect)
-   the ratio of these estimates (Prop. Mediated)

The ACME here is the indirect effect of M (total effect - direct effect)
and thus this value tells us if our mediation effect is significant. If
ACME is significant, but ADE is not, then we have full mediation. If ADE
is significant, but ACME is not, then we have no mediation.

In this case, our **fitMed** model again shows a significant effect of
coffee consumption on the relationship between hours since dawn and
feelings of wakefulness, (ACME = .28, *p* \< .001) with no direct effect
of hours since dawn (ADE = -0.11, *p* = .27) and significant total
effect (*p* \< .05).

We can then bootstrap this comparison to verify this result in
**fitMedBoot** and again find a significant mediation effect (ACME =
.28, *p* \< .001) and no direct effect of hours since dawn (ADE = -0.11,
*p* = .27). However, with increased power, this analysis no longer shows
a significant total effect (*p* = .07).

## Method 3: Mediation using lavaan

```{r, warning=FALSE, message=FALSE}
library(lavaan)

model <-"
Y.wake ~ a*X.hours + b*M.coffee
M.coffee ~ c*X.hours

#indirect effect
ind:=b*c

#total effect
total:=a+(b*c)
"
```

```{r, warning=FALSE, message=FALSE}
medsem<-sem(model = model, data = Meddata, se="bootstrap")

summary(medsem,standardized=T,fit.measures=T,rsquare=T)
```

```{r}
semPaths(object = medsem, whatLabels = "par") # "std" = standardized parameter estimates

```

```{r, warning = FALSE}
mediationPlot(medsem, indirect = TRUE, whatLabels = "est")
```

------------------------------------------------------------------------

# Other types of mediation {.tabset}

## Mediation with Categorical Predictors

When you have categorical predictors with more than 2 levels, you will need to model the mediation effects for each level of that variable. To do that, we're going to dummy code our categorical variable. We're going to use the same dataset but create a 3-level predictor: a lot of sleep, average sleep, little sleep. I know this would be considered ordinal, but let's ignore that for now.

**IMPORTANT NOTES:**

  * When dummy coding a categorical variable with K categories, include only K−1 dummy variables in the model, treating one category as a reference. This avoids the issue of perfect multicollinearity.
    + If all dummy-coded variables for a categorical predictor are included in the model, this violates the assumption of independence because the sum of all dummy variables for a given observation is always 1 (if you include a dummy for each category). In other words, you'll get perfect multicollinearity, where one variable can be perfectly predicted from the others, leading to issues in estimating the model parameters.
    + The interpretation of these coefficients are now in reference to the excluded dummy (i.e., the reference category). 

#### Lavaan

Here, the reference group will be the people who got 'a lot' of sleep (sleep=0)

```{r}
# creating our dataset
set.seed(123)
N <- 100 

# sleep: 0 = a lot, 1 = average, 2 = a little
X.sleep <- sample(0:2, N, replace = TRUE) 
sleep_effect <- -2 
M.coffee <- 0.7 * X.hours + sleep_effect * X.sleep + rnorm(N, 0, 5)
Y.wake <- 0.4 * M.coffee + rnorm(N, 0, 5) 
Meddata_cat <- data.frame(X.hours, X.sleep, M.coffee, Y.wake)
Meddata_cat$sleep <- factor(Meddata_cat$X.sleep)

# dummy code sleep
library(fastDummies)

Meddata_cat <- dummy_cols(Meddata_cat, 
                   select_columns = "X.sleep")

# 'a lot' of sleep is the reference category, so you can omit X.sleep_0 from the model
model_cat <-"
# Direct Effects on wakefulness
Y.wake ~ a1*X.sleep_1 + a2*X.sleep_2 + b*M.coffee

# Effect of sleep on coffee (note: now we use only two dummies, assuming one as reference)
M.coffee ~ c1*X.sleep_1 + c2*X.sleep_2

# Indirect effects (now must include dummy paths for only two levels)
ind1:=b*c1
ind2:=b*c2

# Total effects
total1 := a1 + (b*c1)
total2 := a2 + (b*c2)
"

med_cat<-sem(model = model_cat, data = Meddata_cat)

summary(med_cat,standardized=T,fit.measures=T,rsquare=T)

semPaths(object = med_cat, whatLabels = "par") 

```

#### Mediation package

The process is similar when using the mediation, but note that you'll need to run separate mediations for each level.

```{r}
# Model predicting mediator (coffee)
model_mediator <- lm(M.coffee ~ X.sleep_1 + X.sleep_2, data = Meddata_cat)

# Model predicting outcome (wake), including mediator
model_outcome <- lm(Y.wake ~ X.sleep_1 + X.sleep_2 + M.coffee, data = Meddata_cat)

# average sleep vs a lot of sleep
med.1 <- mediate(model_mediator, model_outcome, treat = "X.sleep_1", mediator = "M.coffee")
summary(med.1)
```

```{r}
# little sleep vs a lot of sleep
med.2 <- mediate(model_mediator, model_outcome, treat = "X.sleep_2", mediator = "M.coffee")
summary(med.2)
```


## Parallel Mediation

```{r}
Meddata$M2.activity <- 2.1 * Meddata$X.hours + rnorm(nrow(Meddata), mean = 0, sd = 1)

summary(lm(Y.wake ~ M2.activity, data = Meddata))
```

```{r}
# Define the model for the outcome variable
parallelModel <- lm(Y.wake ~ X.hours + M.coffee + M2.activity, data = Meddata)

# Define the models for the mediator variables
medModel_coffee <- lm(M.coffee ~ X.hours, data = Meddata)
medModel_activity <- lm(M2.activity ~ X.hours, data = Meddata)

# Perform the mediation analysis for each mediator
mediation_coffee <- mediate(medModel_coffee, parallelModel, 
                                treat = "X.hours", mediator = "M.coffee", 
                                boot = TRUE, sims = 500)

mediation_activity <- mediate(medModel_activity, parallelModel, 
                           treat = "X.hours", mediator = "M2.activity", 
                           boot = TRUE, sims = 500)

# Summarize the mediation analysis results
summary(mediation_coffee)
summary(mediation_activity)
```

```{r}
multipleMediation <- '

# Direct
Y.wake ~ b1 * M.coffee + b2 * M2.activity + c * X.hours
M.coffee ~ a1 * X.hours
M2.activity ~ a2 * X.hours

# Indirect
indirect1 := a1 * b1
indirect2 := a2 * b2

# Total
total := c + (a1 * b1) + (a2 * b2)

# Covariance between mediators
M.coffee ~~ M2.activity
'
fit_mult <- sem(model = multipleMediation, data = Meddata)
summary(fit_mult, fit.measures = TRUE, standardized = TRUE)
```

```{r}
multMed<-sem(model = multipleMediation, data = Meddata, se="bootstrap")

summary(multMed,standardized=T,fit.measures=T,rsquare=T)

semPaths(object = multMed, whatLabels = "std")

mediationPlot(multMed, indirect = TRUE, whatLabels = "par", secondIndirect = TRUE) #standardized estimates
```

```{r}
# Generate random ages between 18 and 65
Meddata$age <- round(runif(N, min = 18, max = 65))

covMediation <- '
# Direct paths
M.coffee ~ a1 * X.hours + age
M2.activity ~ a2 * X.hours + age
Y.wake ~ b1 * M.coffee + b2 * M2.activity + c * X.hours + age

# Covariance between mediators
M.coffee ~~ M2.activity

# Indirect effects
indirect1 := a1 * b1
indirect2 := a2 * b2

# Total effect
total := c + (a1 * b1) + (a2 * b2)
'

fit_cov <- sem(model = covMediation, data = Meddata)

summary(fit_cov, fit.measures = TRUE, standardized = TRUE)  # Adds fit measures and standardized estimates
```

```{r}
covMed<-sem(model = covMediation, data = Meddata, se="bootstrap")

semPaths(object = covMed, whatLabels = "std")
```

## Mediation with binary outcomes

Lavaan automatically detects binary DVs. There's no need to add any
special arguments.

Create binary DV: Pass or fail

```{r}
pass_threshold <- median(Meddata$Y.wake)

# Create binary DV 'pass_fail', where 1 = pass, 0 = fail
Meddata$pass_fail <- ifelse(Meddata$Y.wake > pass_threshold, 1, 0)
```

```{r}
binaryMediation <- '
# Direct paths to mediators
M.coffee ~ a1 * X.hours + age
M2.activity ~ a2 * X.hours + age

# Binary outcome path using logit
pass_fail ~ b1 * M.coffee + b2 * M2.activity + c * X.hours + age

# Covariance between mediators
M.coffee ~~ M2.activity

# Indirect effects
indirect1 := a1 * b1
indirect2 := a2 * b2

# Total effect
total := c + (a1 * b1) + (a2 * b2)
'

# Fitting the model with lavaan
fitBinary <- sem(model = binaryMediation, data = Meddata, estimator = "ML", se = "bootstrap", bootstrap = 1000)

summary(fitBinary, fit.measures = TRUE, standardized = TRUE)
```

```{r}
binMed<-sem(model = fitBinary, data = Meddata, se="bootstrap")

# basic
semPaths(object = binMed, whatLabels = "std")

# change shape and label size
binSem <- semPaths(binMed, 
         whatLabels = "std", 
         edge.label.cex = 0.75,  
         label.cex = 1.5,       
         layout = "spring")
```

Add labels

```{r, message=FALSE, warning=FALSE}

# change node label
binMed_lab <- change_node_label(binSem,
                           c(X.h = "Hours",
                             M.c = "Coffee",
                             M2. = "Activity",
                             ps_ = "Grade"),
                           label.cex = 1.1)
plot(binMed_lab)
```

Indicate which effects are significant

```{r, message=FALSE, warning=FALSE}
sig_plot <- binMed_lab %>%      
  mark_sig(fitBinary) %>% 
  mark_se(fitBinary, sep = "\n")

plot(sig_plot)
```

## Moderated mediation

*credit:
<https://ademos.people.uic.edu/Chapter15.html#31_describe_the_dataset>*

These are challenging to understand, so we're going to walk through a
different example.

Let's examine the question: does spending more time in grad school
predict more offers after graduation? We'll see if this relationship is
explained by number of publications (i.e., the more time spent in grad
school, the more publications one has, and the more publications one
has, the more job offers they get). However, this causal chain may only
work for people who spend their time in graduate school networking.

We are going to simulate a dataset that measured the following:

-   X = Time spent in graduate school (we will change the name to “time”
    when we create the data frame)
-   Z = Time spent networking
-   M = Number of publications in grad school
-   Y = Number of job offers

```{r}
### We are intentionally creating a moderated mediation effect here and we do so below by setting the relationships (the paths) between our causal chain variables and setting the relationships for our interaction terms

set.seed(42) #This makes sure that everyone gets the same numbers generated through rnorm function

a1 = -.59 #Set the path a1 strength (effect of X on M)

a2 = -.17 #Set path a2 strength (effect of Z on M)

a3 = .29 #Set path a3 strength (interaction between X and Z on M)

b = .59 #Set path b strength (effect of M on Y)

cdash1 = .27 #Set path c'1 strength (effect of X on Y)

cdash2 = .01 #Set path c'2 strength (effect of Z on Y)

cdash3 = -.01 #Set path c'3 strength (interaction betwee X and Z on Y)

### Here we are creating the values of our variables for each subject

n <- 200 #Set sample size

X <- rnorm(n, 7, 1) #IV: Time spent in grad school (M = 7, SD = 1)

Z <- rnorm(n, 5, 1) #Moderator: Time spent (hours per week) with Professor Demos in class or in office hours (M = 5, SD = 1)

M <- a1*X + a2*Z + a3*X*Z + rnorm(n, 0, .1) #Mediator: Number of publications in grad school
#The mediator variable is created as a function of the IV, moderator, and their interaction with some random noise thrown in the mix

Y <- cdash1*X + cdash2*Z + cdash3*X*Z + b*M + rnorm(n, 0, .1) #DV: Number of job offers
#Similar to the mediator, the DV is a function of the IV, moderator, their interaction, and the mediator with some random noise thrown in the mix

Success.ModMed <- data.frame(jobs = Y, time = X, pubs = M, network = Z) #Build our data frame and give it recognizable variable names

```

Because we have interaction terms in our regression analyses, we need to
mean center our IV and Moderator (Z)

```{r}
Success.ModMed$time.c <- scale(Success.ModMed$time, center = TRUE, scale = FALSE)[,] #Scale returns a matrix so we have to make it a vector by indexing one column

Success.ModMed$network.c <- scale(Success.ModMed$network, center = TRUE, scale = FALSE)[,]
```

```{r}
Mod.Med.Lavaan <- '
#Regressions
#These are the same regression equations from our previous example
#Except in this code we are naming the coefficients that are produced from the regression equations
#E.g., the regression coefficient for the effect of time on pubs is named "a1"
pubs ~ a1*time.c + a2*network.c + a3*time.c:network.c
jobs ~ cdash1*time.c + cdash2*network.c + cdash3*time.c:network.c + b1*pubs

#Mean of centered network (for use in simple slopes)
#This is making a coefficient labeled "network.c.mean" which equals the intercept because of the "1"
#(Y~1) gives you the intercept, which is the mean for our network.c variable
network.c ~ network.c.mean*1

#Variance of centered network (for use in simple slopes)
#This is making a coefficient labeled "network.c.var" which equals the variance 
#Two tildes separating the same variable gives you the variance
network.c ~~ network.c.var*network.c

#Indirect effects conditional on moderator (a1 + a3*ModValue)*b1
indirect.SDbelow := (a1 + a3*(network.c.mean-sqrt(network.c.var)))*b1 
indirect.SDabove := (a1 + a3*(network.c.mean+sqrt(network.c.var)))*b1

#Direct effects conditional on moderator (cdash1 + cdash3*ModValue)
#We have to do it this way because you cannot call the mean and sd functions in lavaan package
direct.SDbelow := cdash1 + cdash3*(network.c.mean-sqrt(network.c.var)) 
direct.SDabove := cdash1 + cdash3*(network.c.mean+sqrt(network.c.var))

#Total effects conditional on moderator
total.SDbelow := direct.SDbelow + indirect.SDbelow
total.SDabove := direct.SDabove + indirect.SDabove

#Proportion mediated conditional on moderator
#To match the output of "mediate" package
prop.mediated.SDbelow := indirect.SDbelow / total.SDbelow
prop.mediated.SDabove := indirect.SDabove / total.SDabove

#Index of moderated mediation
#An alternative way of testing if conditional indirect effects are significantly different from each other
index.mod.med := a3*b1
'

#Fit model
Mod.Med.SEM <- sem(model = Mod.Med.Lavaan,
                   data = Success.ModMed,
                   se = "bootstrap",
                   bootstrap = 10,
                   fixed.x = FALSE) # pubs should model the variance

#Fit measures
summary(Mod.Med.SEM,
        fit.measures = FALSE,
        standardize = TRUE,
        rsquare = TRUE)

```

-   **pubs \~**
    -   A1 (M \~ X): Significant main effect of time spent in grad
        school on number of publications
    -   A2 (M \~ Z): Significant main effect of time spent networking on
        number of publications
    -   A3 (M \~ X \* Z): Significant interaction between time spent in
        grad school and time spent networking on number of publications
-   **jobs \~**
    -   (cds1) (Y \~ X): Significant main effect of time spent in grad
        school on number of job offers
    -   (cds2) (Y \~ Z): No effect of time spent networking on number of
        job offers
    -   (cds3) (Y \~ M): Significant main effect of number of
        publications on number of job offers
    -   (b1) (Y \~ X \* Z): No interaction between time spent in grad
        school and time spent networking on number of job offers

*To look at the moderator effect, we can use the +/- 1SD from the mean*

-   **those who spend little time networking**
    -   (direct.SDblw) Significant direct effect of time spent in grad
        school on job offers (for those who don’t spend a lot of time
        networking)
    -   (indirect.SDbelow) Significant indirect effect of time spent in
        grad school on job offers through publications (for those who
        don’t spend a lot of time networking)
-   **those who spend a lot of time networking**
    -   (direct.SDabv) Significant direct effect of time spent in grad
        school on job offers (for those who spend a lot of time
        networking)
    -   (indirect.SDabv) Significant indirect effect of time spent in
        grad school on job offers through publications (for those who
        spend a lot of time networking)
-   **what does this mean?**
    -   Time spent in graduate school positively affects the number of
        job offers, both directly and indirectly through the number of
        publications. The strength of this indirect effect is depends on
        the amount of time spent networking.
    -   Specifically, while the mediated path was significant regardless
        of networking time, *the strength of the publications explaining
        the relationship between time spent in grad school and job
        offers was stronger for people who spent a lot of time
        networking.*

```{r}
mm_plot <- semPaths(Mod.Med.SEM, 
         whatLabels = "est", 
         edge.label.cex = 0.75,  
         label.cex = 1.5,       
         layout = "spring",
         intercepts = FALSE)

# change node label
Modmed_lab <- change_node_label(mm_plot,
                           c(jbs = "Y.Jobs",
                             pbs = "M.Pubs",
                             tm. = "X.Time",
                             nt. = "Z.Network",
                             't.:' = "T*N"),
                           label.cex = 1.1)

sig_plot_mm <- Modmed_lab %>%      
  mark_sig(Mod.Med.SEM) %>% 
  mark_se(Mod.Med.SEM, sep = "\n")

plot(sig_plot_mm)
```

```{r}
#Bootstraps
parameterEstimates(Mod.Med.SEM,
                   boot.ci.type = "bca.simple",
                   level = .95, ci = TRUE,
                   standardized = FALSE)[c(19:27),c(4:10)] #We index the matrix to only display columns we are interested in
```

The difference is most likely a result of bootstrap estimation
differences (e.g., lavaan uses bias-corrected but not accelerated
bootstrapping for their confidence intervals)

```{r}
#install.packages("JSmediation")
library(JSmediation)

Success.ModMed$pubs.c <- scale(Success.ModMed$pubs, center = TRUE, scale = FALSE)[,]

moderated_mediation_fit <- 
  mdt_moderated(data = Success.ModMed,
                IV   = time.c,
                DV   = jobs, 
                M    = pubs.c,
                Mod  = network.c)

moderated_mediation_fit %>% add_index(stage = "first")

compute_indirect_effect_for(moderated_mediation_fit, Mod = 1) 
```

------------------------------------------------------------------------

# Nonlinear regression

This dataset has a binary response (outcome, dependent) variable called
admit. There are three predictor variables: gre, gpa and rank. We will
treat the variables gre and gpa as continuous. The variable rank takes
on the values 1 through 4. Institutions with a rank of 1 have the
highest prestige, while those with a rank of 4 have the lowest.

```{r}
mydata <- read.csv("https://stats.idre.ucla.edu/stat/data/binary.csv")

xtabs(~admit + rank, data = mydata)
```

## Logistic regression

```{r simple logistic regression}
mydata$rank <- factor(mydata$rank)
mylogit <- glm(admit ~ gre + gpa + rank, data = mydata, family = "binomial")

summary(mylogit)
```

-   For every one unit change in gre, the log odds of admission (versus
    non-admission) increases by 0.002.
-   For a one unit increase in gpa, the log odds of being admitted to
    graduate school increases by 0.804.
-   The indicator variables for rank have a slightly different
    interpretation. For example, having attended an undergraduate
    institution with rank of 2, versus an institution with a rank of 1,
    changes the log odds of admission by -0.675.

```{r}
confint(mylogit)
```

```{r}
## odds ratios and 95% CI
exp(cbind(OR = coef(mylogit), confint(mylogit)))
```

### Wald-test (like an omnibus test)

**Main effect of rank**

```{r}
library(aod)
wald.test(b = coef(mylogit), Sigma = vcov(mylogit), Terms = 4:6)
```

The chi-squared test statistic of 20.9, with three degrees of freedom is
associated with a p-value of 0.00011 indicating that the overall effect
of rank is statistically significant.

**Main effect of gre**

```{r}
wald.test(b = coef(mylogit), Sigma = vcov(mylogit), Terms = 2)
```

**Main effect of gpa**

```{r}
wald.test(b = coef(mylogit), Sigma = vcov(mylogit), Terms = 3)
```

#### Pseudo-R squared for logisitic regression

```{r}
PseudoR2(mylogit, which = c("CoxSnell","Nagelkerke"))
```

### Graph logistic regression

1.  Start by calculating the predicted probability of the outcome at
    each level of the categorical/ordinal predictor variable and/or
    holding continuous variables at their means.
2.  Create the predicted probabilities using the new dataframe.
3.  Start creating the predicted probability version of your variables
4.  Set the SE to display
5.  Graph

```{r}
# step 1 
newdata1 <- with(mydata,
                 data.frame(gre = mean(gre), gpa = mean(gpa), rank = factor(1:4)))

# step 2
newdata1$rankP <- predict(mylogit, newdata = newdata1, type = "response")
newdata1

# step 3
newdata2 <- with(mydata,
                 data.frame(gre = rep(seq(from = 200, to = 800, length.out = 100), 4),
                            gpa = mean(gpa), rank = factor(rep(1:4, each = 100))))

# step 4
newdata3 <- cbind(newdata2, predict(mylogit, newdata = newdata2, type="link", se=TRUE))
newdata3 <- within(newdata3, {
  PredictedProb <- plogis(fit)
  LL <- plogis(fit - (1.96 * se.fit))
  UL <- plogis(fit + (1.96 * se.fit))
})

# graph
PredProbPlot <- ggplot(newdata3, aes(x = gre, y = PredictedProb)) +
  geom_ribbon(aes(ymin = LL, ymax = UL, fill = rank), alpha = .2) +
  geom_line(aes(colour = rank), size=1) +theme_minimal()

PredProbPlot + ggtitle("Admission to Grad School by Rank")
```

#### Simpler prediction plot

```{r}
library(ggeffects)
plot(ggpredict(mylogit,c("gre","rank")))
```

## Multinomial Regression

The data set contains variables on 200 students. The outcome variable is
**prog**, program type. The predictor variables are social economic
status, **ses**, a three-level categorical variable and writing score,
**write**, a continuous variable.

> (Research Question): When high school students choose the program
> (general, vocational, and academic programs), how do their math and
> science scores and their social economic status (SES) affect their
> decision?

```{r}
hsb <- read.dta("https://stats.idre.ucla.edu/stat/data/hsbdemo.dta")

with(hsb, table(ses, prog))
```

```{r}
# Since we are going to use Academic as the reference group, we need relevel the group.
hsb$prog2 <- relevel(as.factor(hsb$prog), ref = 2)
hsb$ses <- as.factor(hsb$ses)
levels(hsb$prog2)
```

```{r}
# Run a multinomial model
multi_mo <- multinom(prog2 ~ ses + math + science + math*science, data = hsb,model=TRUE)

summary(multi_mo)
```

**Main effects**

```{r}
Anova(multi_mo, type="II")
```

```{r}
PseudoR2(multi_mo, which = c("CoxSnell","Nagelkerke"))
```

```{r}
broom::tidy(multi_mo, conf.int= TRUE, conf.level = 0.95, exponentiate = T)
```

Another way to understand the model using the predicted probabilities is
to look at the averaged predicted probabilities for different values of
the continuous predictor variable math within each level of ses.

```{r}
# Extract coefficients
coef_df <- as.data.frame(coef(multi_mo))
coef_df$Term <- row.names(coef_df)

# Melt the dataframe for ggplot
library(reshape2)
melted_coef_df <- melt(coef_df, id.vars = c("Term", "(Intercept)"))

# Plot using ggplot2
library(ggplot2)
ggplot(melted_coef_df, aes(x = Term, y = value, fill = variable)) +
  geom_bar(stat = "identity", position = position_dodge()) +
  theme_minimal() +
  labs(x = "Term", y = "Coefficient", fill = "Outcome") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

```

```{r}
plot(ggpredict(multi_mo,c("ses", "math")))
```

#### Write-up

> (Research Question): When high school students choose the program
> (general, vocational, and academic programs), how do their math and
> science scores and their social economic status (SES) affect their
> decision?
>
> > A one-unit increase in math is associated with the decrease in the
> > log odds of being in general program vs. academic program in the
> > amount of .19 (one-unit increase in the variable math is .83 for
> > being in general program vs. academic program).
>
> > Students in the highest social status level (SES = 3), compared to
> > the lowest (SES = 1), are less likely to be in the general program
> > compared to the academic one. The chance decreases by about 1.125
> > times, b = -1.125, Wald χ2(1) = -5.27, p \<.001. This means their
> > odds are about 0.325 times lower, making students from lower social
> > status more inclined to pick the general program over the academic
> > one.
>
> > Similarly, for high SES students (compared to low), the likelihood
> > of being in the vocational program instead of the academic program
> > drops by 0.56 times, b = -0.56, Wald χ2(1) = -2.82, p \< 0.01. In
> > other words, lower-status students (compared to high SES) prefer the
> > vocational program over the academic one.

## Poisson regression

Here, we're looking at whether prog and math predict number of awards

```{r}
p <- read.csv("https://stats.idre.ucla.edu/stat/data/poisson_sim.csv")
p <- within(p, {
  prog <- factor(prog, levels=1:3, labels=c("General", "Academic", 
                                                     "Vocational"))
  id <- factor(id)
})
summary(p)
```

```{r}
ggplot(p, aes(num_awards, fill = prog)) +
  geom_histogram(binwidth=.5, position="dodge") + theme_classic()
```

```{r}
summary(m1 <- glm(num_awards ~ prog + math, family="poisson", data=p))
```

Cameron and Trivedi (2009) recommended using robust standard errors for
the parameter estimates to control for mild violation of the
distribution assumption that the variance equals the mean.

```{r}
cov.m1 <- vcovHC(m1, type="HC0")
std.err <- sqrt(diag(cov.m1))
r.est <- cbind(Estimate= coef(m1), "Robust SE" = std.err,
"Pr(>|z|)" = 2 * pnorm(abs(coef(m1)/std.err), lower.tail=FALSE),
LL = coef(m1) - 1.96 * std.err,
UL = coef(m1) + 1.96 * std.err)

r.est
```

#### Plot predictions

```{r}
## calculate and store predicted values
p$phat <- predict(m1, type="response")

## order by program and then by math
p <- p[with(p, order(prog, math)), ]

## create the plot
ggplot(p, aes(x = math, y = phat, colour = prog)) +
  geom_point(aes(y = num_awards), alpha=.5, position=position_jitter(h=.2)) +
  geom_line(size = 1) + theme_classic() +
  labs(x = "Math Score", y = "Expected number of awards")
```

#### Write up

> Being in an academic program was associated with a significant
> increase in the number of awards, b = 1.084, SE = 0.358, z = 3.025, p
> = 0.00248, indicating that students in academic programs tend to
> receive more awards than those in general programs, holding math
> scores constant.
>
> Being in a vocational program did not significantly predict the number
> of awards compared to being in a general program, b = 0.370, SE =
> 0.441, z = 0.838, p = 0.40179, suggesting no significant difference in
> the expected count of awards between vocational and general program
> students, again holding math scores constant.
>
> Math scores were also a significant predictor of the number of awards,
> b = 0.07015, SE = 0.01060, z = 6.619, p \< 0.0001, suggesting that,
> regardless of program type, an increase in math scores is associated
> with an increase in the expected number of awards.

## Ordinal regression

```{r}
library(MASS) # For ordinal logistic regression (polr)

# Generate example data
set.seed(123)
data <- data.frame(
  StudyHours = rnorm(100, mean = 5, sd = 2), # Simulating study hours
  Performance = ordered(sample(1:5, 100, replace = TRUE), levels = c(1, 2, 3, 4, 5), labels = c("Poor", "Below Average", "Average", "Above Average", "Excellent"))
)

# Fit an ordinal logistic regression model
model <- polr(Performance ~ StudyHours, data = data)

summary(model)

```

#### Get p-values

```{r}
## store table
(ctable <- coef(summary(model)))

## calculate and store p values
p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2

## combined table
(ctable <- cbind(ctable, "p value" = p))
```

The significance of "Above Average\|Excellent" suggests that study hours
become more influential in determining whether students achieve Above
Average vs Excellent.

#### Plot ordinal

```{r}

# Create a sequence of study hours for prediction
new_data <- data.frame(StudyHours = seq(min(data$StudyHours), max(data$StudyHours), length.out = 100))

# Predict probabilities for each performance category
predicted_probs <- as.data.frame(predict(model, newdata = new_data, type = "probs"))

# Rename the columns for clarity
colnames(predicted_probs) <- c("Poor", "Below Average", "Average", "Above Average", "Excellent")

# Create a visualization
ggplot(predicted_probs, aes(x = new_data$StudyHours)) +
  geom_line(aes(y = `Poor`, color = "Poor"), size = 1) +
  geom_line(aes(y = `Below Average`, color = "Below Average"), size = 1) +
  geom_line(aes(y = `Average`, color = "Average"), size = 1) +
  geom_line(aes(y = `Above Average`, color = "Above Average"), size = 1) +
  geom_line(aes(y = `Excellent`, color = "Excellent"), size = 1) +
  labs(title = "Ordinal Logistic Regression: Predicting Student Performance",
       x = "Study Hours",
       y = "Predicted Probability") +
  scale_color_manual(values = c("Poor" = "#1f77b4", 
                                "Below Average" = "#ff7f0e", 
                                "Average" = "#2ca02c", 
                                "Above Average" = "#d62728", 
                                "Excellent" = "#9467bd"),
                     name = "Performance Level",
                     limits = c("Excellent","Above Average", "Average", "Below Average", "Poor")) + # Explicitly set the order
  theme_minimal()

```


