ANOVA with repeated measures and TukeyHSD post-hoc test in R-CodePudding

I would like to do Tukey HSD post hoc tests for a repeated measure ANOVA. The entered formula "TukeyHSD" returns me an error. I can't find the answer in the forum. Can I ask for help?

"treat" is repeated measures factor, "vo2" is dependent variable.

Below is a script that is producing this error:

my_data <- data.frame(
  stringsAsFactors = FALSE,
  id = c(1L,2L,3L,4L, 5L,1L,2L,3L,4L,5L,1L,2L,3L,4L,5L,1L,2L,3L,4L,5L),
  treat = c("o","o","o","o","o","j","j","j","j","j","z","z","z","z","z","w","w","w","w","w"),
  vo2 = c("47.48","42.74","45.23","51.65","49.11","51.00","43.82","49.88","54.61","52.20","51.31",
          "47.56","50.69","54.88","55.01","51.89","46.10","50.98","53.62","52.77"))

summary(rm_result <- aov(vo2~factor(treat) Error(factor(id)), data = my_data))
TukeyHSD(rm_result, "treat", ordered = TRUE)

CodePudding user response：

TukeyHSD() can't work with the aovlist result of a repeated measures ANOVA. As an alternative, you can fit an equivalent mixed effects model with e.g. lme4::lmer() and do the post-hoc tests with multcomp::glht().

my_data$vo2 <- as.numeric(my_data$vo2)
my_data$treat <- factor(my_data$treat)
m <- lme4::lmer(vo2 ~ treat   (1|id), data = my_data)
summary(multcomp::glht(m, linfct=mcp(treat="Tukey")))

# Simultaneous Tests for General Linear Hypotheses
# 
# Multiple Comparisons of Means: Tukey Contrasts
# 
# 
# Fit: lmer(formula = vo2 ~ treat   (1 | id), data = my_data)
# 
# Linear Hypotheses:
#            Estimate Std. Error z value Pr(>|z|)    
# o - j == 0   -3.060      0.583  -5.248   <0.001 ***
# w - j == 0    0.770      0.583   1.321   0.5497    
# z - j == 0    1.588      0.583   2.724   0.0327 *  
# w - o == 0    3.830      0.583   6.569   <0.001 ***
# z - o == 0    4.648      0.583   7.972   <0.001 ***
# z - w == 0    0.818      0.583   1.403   0.4974    
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# (Adjusted p values reported -- single-step method)

Comparison of the mixed effects model's ANOVA table with your repeated measures ANOVA results shows that both approaches are equivalent in how they treat the treat variable:

anova(m)
# Analysis of Variance Table
#       npar Sum Sq Mean Sq F value
# treat    3 61.775  20.592   24.23

summary(rm_result)
# Error: factor(id)
#           Df Sum Sq Mean Sq F value Pr(>F)
# Residuals  4  175.9   43.98               
# 
# Error: Within
#               Df Sum Sq Mean Sq F value   Pr(>F)    
# factor(treat)  3  61.78   20.59   24.23 2.22e-05 ***
# Residuals     12  10.20    0.85                     
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1