这一章节，主要介绍模型中的定义，什么是「变量」，什么是「因子」，什么是「水平」等等。
1. 标题
2. 几个概念
「什么是因子，什么是水平？」比如，性别包括男性和女性，这里，性别是「因子」，男性和女性为因子的「水平」。
「因子间的交互」
3. 什么是平衡数据
平衡数据：
- 因子是平衡的，那么每个水平的个数是相等的
- 如果两因子交互是平衡的，那么每个因子也是平衡的
如果数据是平衡的，那么估算出的固定因子效应值，等于其平均值，其显著性检验变成了F检验。
如果数据是非平衡的，固定因子的效应值会进行校正，显著性方法也有所变化。所以数据非平衡时，混合线性模型更适合分析。
4. R代码操作
对应的R代码
代码语言：javascript复制################################################################
### 02429 - Analysis of correlated data: Mixed Linear Models ###
### R-script for eNote-2 ###
################################################################
require(diagram) # For factor structure diagrams
## Create the list of factor names with indices
names <- c(expression("[I]"[24]^{30}),
expression(atm:temp[2]^{6}),
expression(atm[1]^{2}),
expression(temp[2]^{3}),
expression(0[1]^{1}))
## As there are 5 factors, create the 5x5 matrix of zeros
M <- matrix(nrow = 5, ncol = 5, byrow = TRUE, data = 0)
## Envision the structure: e.g., I need an arrow from the first
## factor in my list to the second, so assign something to M[2,1]
M[2, 1] <- M[3,2] <- M[4,2] <- M[5,3] <- M[5,4] <- ""
## Make the diagram:
plotmat(M, pos = c(1, 1, 2, 1), name = names, lwd = 2,
box.lwd = 1, cex.txt = 1, box.size = 0.1, box.type = "square",
box.prop = 0.4, arr.type = "triangle", curve = 0)
## Function for rotation of factor structure diagram
matrix_position <- function(pos_vec) {
n <- sum(pos_vec) # rows
m <- length(pos_vec)-2 # inner layers
d_hori <- 0.8/(m 1)
bot <- 0.1; mid <- 0.5; top <- 0.9
pos_mat <- matrix(nrow=n, ncol=2)
pos_mat[1,1] <- bot; pos_mat[n,1] <- top
pos_mat[1,2] <- pos_mat[n,2] <- mid
cum_pos <- cumsum(pos_vec)
for (i in 1:m) {
n_vert <- pos_vec[i 1]
d_vert <- 0.8 / (n_vert 1)
for (j in 1:n_vert){
pos_mat[cum_pos[i] j, 2] <- 0.1 j*d_vert
pos_mat[cum_pos[i] j, 1] <- 0.1 i*d_hori
}
}
return(pos_mat)
}
## Rotated factor structure diagram
plotmat(M, pos = matrix_position(c(1, 1, 2, 1)), name = names, lwd = 2,
box.lwd = 1, cex.txt = 1, box.size = 0.1, shadow.size = 0,
box.type = "square", box.prop = 0.5, arr.type = "triangle",
curve = 0)
## Create the list of factor names with indices
names <- c(expression("[I]"[266]^{300}),
expression(depth:width[8]^{15}),
expression("[plank]"[19]^{20}),
expression(width[2]^{3}),
expression(depth[4]^{5}),
expression(0[1]^{1}))
## Since there are 6 factors, create the 6x6 matrix of zeros
M <- matrix(nrow = 6, ncol = 6, byrow = TRUE, data = 0)
## Envision the structure: E.g., I need an arrow from the first factor level to the second,
## so assign something to M[2,1], etc.
M[2, 1] <- M[3, 1] <- M[4, 2] <- M[5, 2] <- ""
M[6, 3] <- M[6, 4] <- M[6, 5] <- ""
## Make the diagram
plotmat(M, pos = c(1, 1, 3, 1), name = names, lwd = 2,
box.lwd = 1, cex.txt = 1, box.size = 0.1, shadow.size = 0,
box.type = "square", box.prop = 0.4, arr.type = "triangle",curve=0)
## Create the list of factor names with indices
names <- c(expression("[I]"[24]^{30}),
expression(atm:temp[2]^{6}),
expression(atm[1]^{2}),
expression(temp[2]^{3}),
expression(0[1]^{1}))
## Define the coordinates of all the terms in a grid, here (2x8; 2x8):
x <- c(2, 4, 6, 6, 8)
y <- c(5, 5, 3, 7, 5)
## Make an empty plot without any arrows or text:
plot(NA, NA, xlim = c(2, 8), ylim = c(2, 8), type = "n", axes = F,
xlab = "", ylab = "")
text(x, y, names) # Add text according to the 'names' vector
## Define coordinates for the beginning and end points,
## (x0, y0) and (x1, y1), for 5 arrows:
x0 <- c(1.8, 4.2, 4.2, 6, 6) .5
y0 <- c(5, 5, 5, 3, 7)
x1 <- c(2.7, 5, 5, 7.2, 7.2) .5
y1 <- c(5, 3, 7, 5, 5)
arrows(x0, y0, x1, y1, length = 0.1) # 'length' applies to arrrow head
draw.arrows <- function(n) {
ret <- locator(2*n)
o <- (1:(2*n)) %% 2 == 1
e <- (1:(2*n)) %% 2 == 0
x0 <- ret$x[o]
y0 <- ret$y[o]
x1 <- ret$x[e]
y1 <- ret$y[e]
return(list(x0 = x0, y0 = y0, x1 = x1, y1 = y1))
}
plot(NA, NA, xlim = c(2, 8), ylim = c(2, 8), type = "n", axes = F,
xlab = "", ylab = "")
text(x, y, names)
arr <- draw.arrows(5)
arrows(arr$x0, arr$y0, arr$x1, arr$y1, length = .1)
pdf("./mydiagram.pdf") # This is the path/name_of_figure
plot(NA, NA, xlim = c(2, 8), ylim = c(2, 8), type = "n", axes = F,
xlab = "", ylab = "")
text(x, y, names)
arrows(arr$x0, arr$y0, arr$x1, arr$y1, length = .1)
# Close graphics device:
dev.off() # Only now, the figure is actually saved.混合线性模型学习笔记1
混合线性模型学习笔记2
