循环二次回归

Question

以下是我的数据框

data <- data.frame(y = rep(1:10, times = 4), dataID = rep(1:4, each = 10),x1 = rnorm(40), x2 = rnorm(40), x3 = rnorm(40))

对于每个dataID和x组合，我有兴趣计算y与每个x之间的线性回归的Rsquared

variable <- c("x1", "x2", "x3", "x4")

for(v in seq_along(variable)){

 varref <- variable[v]

 temp <- data %>% dplyr::select(y, dataID, varref)

 modID <- sort(unique(temp$dataID))

for(m in seq_along(modID)){

  modRef <- modID[m]
  tempMod <- temp %>% dplyr::filter(dataID == modRef) %>% dplyr::select(-dataID)
  Rsq <- summary(lm(y ~ ., data = tempMod))$adj.r.squared
}

但是，我真正想做的是使线性和非线性项回归。 所以我想知道是否有任何办法可以指代这样的非线性术语：

 Rsq <- summary(lm(y ~ . + I(.^2), data = tempMod))$adj.r.squared

Answer 1

您可以首先根据datID split数据。

sl <- split(dat[-2], dat$datID)

然后将其堆叠以在列出的子集中获得此格式。

#         values ind
# 1  -0.18558347  x1
# 2   0.26342365  x1
# 3   2.24365427  x1
# ....

l <- lapply(sl, function(x) {
  st <- stack(x, 2:4)
  return(cbind(y=x$y, st))
})

作为第三步，使用by分别为每个x*列进行回归，从而为您提供所需的调整。 r-平方矩阵，其中datID为列， x*为行。

sapply(l, function(x) 
  by(x, x$ind, function(i)
    summary(lm(y ~ values, i))$adj.r.squared))
#              1           2            3          4
# x1 -0.02913955 -0.07963248 -0.002224305 0.07005255
# x2 -0.11442395  0.13642959 -0.116281328 0.21777396
# x3  0.15864022 -0.11180017  0.110556373 0.18661920

您可以轻松地验证结果。

d1 <- dat[dat$datID == 1, c("y", "x1")]
summary(lm(y ~ x1, d1))$adj.r.squared
# [1] -0.02913955

可以看到，结果应该与矩阵的第一个单元相同。

因此与多项式：

sapply(l, function(x) 
  by(x, x$ind, function(i)
    summary(lm(y ~ values + I(values^2), i))$adj.r.squared))
#              1           2           3          4
# x1 -0.09385569 -0.15431438 -0.13778041 0.61666182
# x2 -0.12810364  0.06199001 -0.17033677 0.16826139
# x3  0.32189185 -0.26710528  0.04131524 0.07438912

数据

dat <- structure(list(y = c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 
1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 
6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L), 
    datID = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 
    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
    3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L), x1 = c(-0.185583474894103, 
    0.263423651143744, 2.2436542652316, -1.13150593879308, -1.03459059777182, 
    -1.0188653780855, 1.77189001207599, -0.934738205360317, -0.666096892490933, 
    -0.826042921788607, -0.272687984798706, -1.09852037093336, 
    0.46071342230167, 0.268619377702867, -0.328748146462296, 
    1.53440197834959, -0.220853326721626, -0.808382808810487, 
    -1.66645442449068, -0.242353150310531, 1.26231491749131, 
    0.162668675840026, 0.904121249800934, 0.182921809090968, 
    0.0976287057955422, -0.85694452908352, 0.351871098571782, 
    1.0762092522706, -1.11524095896311, 0.656514413311347, -0.384391504028304, 
    0.528952365385126, -0.151039712939782, -1.21953511523724, 
    0.976270995535166, -1.04402181901669, -1.37102481436038, 
    1.42117000396589, 0.912663580389998, 1.4754732274035), x2 = c(0.0402247269190048, 
    1.33038146656669, -0.459598594357653, -0.856969098432259, 
    0.228451646834162, -0.143028413102539, -1.70899900410409, 
    0.507370783610232, 1.56538440117379, -0.951401815451773, 
    -0.393071689633881, -0.297290136122118, 0.828629815124767, 
    0.515465904120197, 0.190957567662703, 1.31797724653282, 0.747333126551401, 
    1.80770651506827, -0.0692143782238828, 0.733652510844958, 
    0.513558767430303, -0.20007253887957, -0.96235732491512, 
    0.0696221474571983, 0.420165653583179, 0.575500351812627, 
    -3.10456905099436, -1.12954301022196, -0.0133568751505841, 
    0.872703653757334, -2.16354318496144, -0.040885605623714, 
    -2.23800995886235, 0.0875803347755469, 0.334286223450742, 
    1.14624718629833, 1.73296419775862, 0.630121428827583, -0.0854394504507166, 
    -0.119157739756379), x3 = c(0.761736068860907, -0.407127443123656, 
    0.35298681720387, -0.618056268737422, 0.990213082637937, 
    1.3715711543413, -0.389277775804358, -0.332620507679104, 
    -0.705017421192073, -1.38091039816317, -0.190763711175575, 
    -0.489473208003468, -0.637223536105616, 3.45385530080228, 
    -0.159752883157984, 1.51368282996416, -0.128118214564304, 
    1.11468646349289, -1.79708316700774, -0.0857055812374004, 
    0.496044729769967, -1.87377039638354, -1.36550978490534, 
    0.457670667628235, -1.53146832089459, 2.04124827349235, 1.07993603816386, 
    0.0927402664330579, 1.02713895045668, 0.359269719833989, 
    0.886254022672678, -0.0513908691703132, 0.0652030406719866, 
    -0.744441295151328, 0.988314721587972, -0.275845245520699, 
    0.611272789477384, -1.56892502735795, -0.480009166030005, 
    -0.755614369802782)), class = "data.frame", row.names = c(NA, 
-40L))

Answer 2

考虑构建x和x^2项的字符串公式：

variable <- c("x1", "x2", "x3", "x4")    
formulas_vec <- paste0("y ~ ", variable, " + ", variable, "^2")
formulas_vec
# [1] "y ~ x1 + x1^2" "y ~ x2 + x2^2" "y ~ x3 + x3^2" "y ~ x4 + x4^2"

然后，用sapply迭代地运行此字符向量，以在by内部调用lm公式（该函数通过一个或多个因子对数据帧进行子集化，并传递给方法）：

by_list <- by(data, data$dataID, function(sub)    
    sapply(formulas_vec, function(f) summary(lm(as.formula(f), data = sub))$adj.r.squared)
)
by_list
# data$dataID: 1
# y ~ x1 + x1^2 y ~ x2 + x2^2 y ~ x3 + x3^2 y ~ x4 + x4^2 
#    0.09630843   -0.10987047    0.19007264   -0.01738122 
# ------------------------------------------------------------ 
# data$dataID: 2
# y ~ x1 + x1^2 y ~ x2 + x2^2 y ~ x3 + x3^2 y ~ x4 + x4^2 
#   -0.04974500   -0.08639353   -0.10195335    0.02649648 
# ------------------------------------------------------------ 
# data$dataID: 3
# y ~ x1 + x1^2 y ~ x2 + x2^2 y ~ x3 + x3^2 y ~ x4 + x4^2 
#    0.08430858    0.41739019   -0.02605365   -0.11197322 
# ------------------------------------------------------------ 
# data$dataID: 4
# y ~ x1 + x1^2 y ~ x2 + x2^2 y ~ x3 + x3^2 y ~ x4 + x4^2 
#   -0.12424060   -0.11589655   -0.12129724   -0.08263092 

adj_r_matrix <- do.call(rbind, by_list)
adj_r_matrix

#   y ~ x1 + x1^2 y ~ x2 + x2^2 y ~ x3 + x3^2 y ~ x4 + x4^2
# 1    0.09630843   -0.10987047    0.19007264   -0.01738122
# 2   -0.04974500   -0.08639353   -0.10195335    0.02649648
# 3    0.08430858    0.41739019   -0.02605365   -0.11197322
# 4   -0.12424060   -0.11589655   -0.12129724   -0.08263092

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