Hello;
I am having a problems with the interpretation of models using ordered or
unordered predictors.
I am running models in lmer but I will try to give a simplified example
data set using lm.
Both in the example and in my real data set I use a predictor variable
referring to 3 consecutive days of an experiment. It is a factor, and I
thought it would be more correct to consider it ordered.
Below is my example code with my comments/ideas along it.
Can someone help me to understand what is happening?
Thanks a lot in advance;
Catarina Miranda
y<-c(72,25,24,2,18,38,62,30,78,34,67,21,97,79,64,53,27,81)
Day<-c(rep("Day 1",6),rep("Day 2",6),rep("Day 3",6))
dataf<-data.frame(y,Day)
str(dataf) #Day is not ordered
#'data.frame': 18 obs. of 2 variables:
# $ y : num 72 25 24 2 18 38 62 30 78 34 ...
# $ Day: Factor w/ 3 levels "Day 1","Day 2",..: 1 1 1 1 1 1 2 2 2 2 ...
summary(lm(y~Day,data=dataf)) #Day 2 is not significantly different from
Day 1, but Day 3 is.
#
#Call:
#lm(formula = y ~ Day, data = dataf)
#
#Residuals:
# Min 1Q Median 3Q Max
#-39.833 -14.458 -3.833 13.958 42.167
#
#Coefficients:
# Estimate Std. Error t value Pr(>|t|)
#(Intercept) 29.833 9.755 3.058 0.00797 **
#DayDay 2 18.833 13.796 1.365 0.19234
#DayDay 3 37.000 13.796 2.682 0.01707 *
#---
#Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
#
#Residual standard error: 23.9 on 15 degrees of freedom
#Multiple R-squared: 0.3241, Adjusted R-squared: 0.234
#F-statistic: 3.597 on 2 and 15 DF, p-value: 0.05297
#
dataf$Day<-ordered(dataf$Day)
str(dataf) # "Day 1"<"Day 2"<"Day 3"
#'data.frame': 18 obs. of 2 variables:
# $ y : num 72 25 24 2 18 38 62 30 78 34 ...
# $ Day: Ord.factor w/ 3 levels "Day 1"<"Day 2"<..: 1 1 1 1 1 1 2 2 2 2 ...
summary(lm(y~Day,data=dataf)) #Significances reversed (or "Day.L" and
"Day.Q" are not sinonimous "Day 2" and "Day 3"?): Day 2 (".L") is
significantly different from Day 1, but Day 3 (.Q) isn't.
#Call:
#lm(formula = y ~ Day, data = dataf)
#
#Residuals:
# Min 1Q Median 3Q Max
#-39.833 -14.458 -3.833 13.958 42.167
#
#Coefficients:
# Estimate Std. Error t value Pr(>|t|)
#(Intercept) 48.4444 5.6322 8.601 3.49e-07 ***
#Day.L 26.1630 9.7553 2.682 0.0171 *
#Day.Q -0.2722 9.7553 -0.028 0.9781
#---
#Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
#
#Residual standard error: 23.9 on 15 degrees of freedom
#Multiple R-squared: 0.3241, Adjusted R-squared: 0.234
#F-statistic: 3.597 on 2 and 15 DF, p-value: 0.05297
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