LME_tutorial

LME tutorial 1

想要探究男性 VS 女性的 voice pitch 是否有差别
- 如果有差别，差别是多大？
招募一群男性和一群女性，让两组人都发音“mama”, 测量并记录下他们的 voice pitch
- Hz 的值越大，pitch 越高

Linear model comes in

Give you some values about voice pitch for males and females
Also give you probability value as to how likely those values are

# pitch predicted by sex
pitch ~ sex

The left is the dependent var (the thing you measure), the right one is the independent var (the fixed effect)
但是，决定 pitch 的因素又不止性别，还有 language, dialect, personality 等因素，所以我们的 model 要加上代表 random factors 的 ε

pitch ~ sex + ε

这个 linear model 就是我们想要构建的，右边由两部分因素组成
- Sex 就是 fixed effect, 是这个 model 的 structural or systematic part
- ε 是 random part, 是这个 model 的 probabilistic part

Start in R

Input the data

setwd("E:/R/lme_learning")

library(lme4)
library(ggplot2)
library(dplyr)

pitch = c(233, 204, 242, 130, 112, 142)
sex = c(rep("female", 3), rep("male", 3))

my.df = data.frame(sex, pitch)

Proceed with the linear model, feed it into the lm() function

xmdl <- lm(pitch ~ sex, my.df)
summary(xmdl)

Call: remind you of the model formula that you entered
Residuals: discuss later
Coefficients of the fixed effects: discuss later
Overall results
- Multiple R-squared: 即 R², which is a measure of "variance explained"
  - R² values range from 0 to 1
  - Our R² is 0.921, quite high, means "92.1% of the stuff that is happening in our dataset is explained by our model"
  - → so R² reflects 92.1% variance in our data is explained by differences between males and females
- Adjusted R-squared: R²_adj, it not only looks at how much variance is explained, but also how many fixed effects you used to do the explaining
  - 当你有很多 fixed effects 的时候，R²_adj有可能会变低
- Significance
  - P-value: the probability under the condition that the null hypothesis is true
    原假设（“sex has NO effect on pitch”）为真的概率
  - 但注意区别 significance of the overall model VS p-value of individual coefficients
    - Significance of the overall model 是最底部的这个 p-value
    - P-value of individual coefficients 是 Coefficients table 里面的
      - 由于现在的 model 只有一个 fixed effect，所以 p-value for this individual coefficient 与 p-value for the overall model 是相同的，都是 0.00241
      - 如果你有好几个 fixed effects, p-values for individual coefficient 会与 p-value for the overall model 有差异
      - 但是为什么这里是 sexmale, 而不是 sex?
        
        Female 去哪里了？
        
        因为 Estimate for " (Intercept)" 是 estimate for the female category
        
        而 Estimate for "sexmale" 是 estimate for the difference between the male and the female category
        
        mean(my.df[my.df$sex == "female", ]$pitch 算出 female 组的 mean pitch = 226.33
        
        同理，算出 male 组的 mean pitch = 128
        
        Estimate for "sexmale" = $$128 - 226.33 = -98.33 $$
- F-value and degrees of freedom
  - 如果你用的是 general linear model analysis，这个 F-value 在汇报结果时要用到
  - 如果你想汇报你的结果 is significant, 可以照这么写：
    - We constructed a linear model of pitch as a function of sex. This model was significant (F (1, 4) = 46.61, p < 0.01).