如何从 plm FE 回归中获得 R2 和整体 R2？

Question

有没有办法让plm() 为我计算 R2 和总体 R2 之间的值并将它们包含在 summary() 输出中？

要澄清我在 R2 之间、整体和内部的意思，请参阅StackExchange 上的此答案。

我的理解是 plm 只在 R2 内计算。 我正在模型中运行双向效果。

一个随机的例子（改编自here）：

library(plm)
# Create some random data
set.seed(1) 
x=rnorm(100); fe=rep(rnorm(10),each=10); id=rep(1:10,each=10); ti=rep(1:10,10); e=rnorm(100)
y=x+fe+e

data=data.frame(y,x,id,ti)

# Get plm within R2
reg=plm(y~x,model="within",index=c("id","ti"), effect = "twoways", data=data)
summary(reg)$r.squared

我现在也想得到整体和R2之间的：

# Pooled Version (overall R2)
reg1=lm(y~x)
summary(reg1)$r.squared

# Between R2
y.means=tapply(y,id,mean)[id]
x.means=tapply(x,id,mean)[id]

reg2=lm(y.means~x.means)
summary(reg3)$r.squared

Answer 1

“内部”估计量相当于最小二乘虚拟变量估计量，您可以通过 OLS 进行估计。这报告了一个整体的 r 平方（......与上面 paqmo 的函数给出的不同 - 也许他们可以澄清一下？）

lsdv<-lm(y~-1+x+as.factor(id)+as.factor(ti),data=data)
summary(lsdv)

请注意，x 的估计系数是相同的。

Answer 2

{plm} 似乎无法报告整体或在引用-取消引用的 R 平方值内。您可以通过创建自定义 summary 和 print 方法来破解它：

summary.plm.full <- function (object, vcov = NULL, ...) 
{
  vcov_arg <- vcov

  #add plm::: for plm functions so they are calllex correctly
  model <- plm:::describe(object, "model")
  effect <- plm:::describe(object, "effect")
  random.method <- plm:::describe(object, "random.method")
  object$r.squared <- c(rsq = r.squared(object), 
                        adjrsq = r.squared(object, dfcor = TRUE),
                        # add the two new r squared terms here
                        rsq_overall = r.squared(object, model = "pooled"),
                        rsq_btw = r.squared(update(object, effect = "individual", model = "between")))

  use.norm.chisq <- FALSE
  if (model == "random") 
    use.norm.chisq <- TRUE
  if (length(formula(object))[2] >= 2) 
    use.norm.chisq <- TRUE
  if (model == "ht") 
    use.norm.chisq <- TRUE
  object$fstatistic <- pwaldtest(object, test = ifelse(use.norm.chisq, 
                                                       "Chisq", "F"), vcov = vcov_arg)
  if (!is.null(vcov_arg)) {
    if (is.matrix(vcov_arg)) 
      rvcov <- vcov_arg
    if (is.function(vcov_arg)) 
      rvcov <- vcov_arg(object)
    std.err <- sqrt(diag(rvcov))
  }
  else {
    std.err <- sqrt(diag(stats::vcov(object)))
  }
  b <- coefficients(object)
  z <- b/std.err
  p <- if (use.norm.chisq) {
    2 * pnorm(abs(z), lower.tail = FALSE)
  }
  else {
    2 * pt(abs(z), df = object$df.residual, lower.tail = FALSE)
  }
  object$coefficients <- cbind(b, std.err, z, p)
  colnames(object$coefficients) <- if (use.norm.chisq) {
    c("Estimate", "Std. Error", "z-value", "Pr(>|z|)")
  }
  else {
    c("Estimate", "Std. Error", "t-value", "Pr(>|t|)")
  }
  if (!is.null(vcov_arg)) {
    object$rvcov <- rvcov
    rvcov.name <- paste0(deparse(substitute(vcov)))
    attr(object$rvcov, which = "rvcov.name") <- rvcov.name
  }
  object$df <- c(length(b), object$df.residual, length(object$aliased))
  class(object) <- c("summary.plm.full", "plm", "panelmodel")
  object
}

对于打印：

print.summary.plm.full <- function (x, digits = max(3, getOption("digits") - 2), width = getOption("width"), 
          subset = NULL, ...) 
{
  formula <- formula(x)
  has.instruments <- (length(formula)[2] >= 2)
  effect <- plm:::describe(x, "effect")
  model <- plm:::describe(x, "model")
  if (model != "pooling") {
    cat(paste(plm:::effect.plm.list[effect], " ", sep = ""))
  }
  cat(paste(plm:::model.plm.list[model], " Model", sep = ""))
  if (model == "random") {
    ercomp <- describe(x, "random.method")
    cat(paste(" \n   (", random.method.list[ercomp], "'s transformation)\n", 
              sep = ""))
  }
  else {
    cat("\n")
  }
  if (has.instruments) {
    cat("Instrumental variable estimation\n")
    if (model != "within") {
      ivar <- plm:::describe(x, "inst.method")
      cat(paste0("   (", plm:::inst.method.list[ivar], "'s transformation)\n"))
    }
  }
  if (!is.null(x$rvcov)) {
    cat("\nNote: Coefficient variance-covariance matrix supplied: ", 
        attr(x$rvcov, which = "rvcov.name"), "\n", sep = "")
  }
  cat("\nCall:\n")
  print(x$call)
  cat("\n")
  pdim <- pdim(x)
  print(pdim)
  if (model %in% c("fd", "between")) {
    cat(paste0("Observations used in estimation: ", nobs(x), 
               "\n"))
  }
  if (model == "random") {
    cat("\nEffects:\n")
    print(x$ercomp)
  }
  cat("\nResiduals:\n")
  df <- x$df
  rdf <- df[2L]
  if (rdf > 5L) {
    save.digits <- unlist(options(digits = digits))
    on.exit(options(digits = save.digits))
    print(plm:::sumres(x))
  }
  else if (rdf > 0L) 
    print(residuals(x), digits = digits)
  if (rdf == 0L) {
    cat("ALL", x$df[1L], "residuals are 0: no residual degrees of freedom!")
    cat("\n")
  }
  if (any(x$aliased, na.rm = TRUE)) {
    naliased <- sum(x$aliased, na.rm = TRUE)
    cat("\nCoefficients: (", naliased, " dropped because of singularities)\n", 
        sep = "")
  }
  else cat("\nCoefficients:\n")
  if (is.null(subset)) 
    printCoefmat(coef(x), digits = digits)
  else printCoefmat(coef(x)[subset, , drop = FALSE], digits = digits)
  cat("\n")
  cat(paste("Total Sum of Squares:    ", signif(plm:::tss.plm(x), digits), 
            "\n", sep = ""))
  cat(paste("Residual Sum of Squares: ", signif(deviance(x), 
                                                digits), "\n", sep = ""))
  cat(paste("R-Squared:      ", signif(x$r.squared[1], digits), 
            "\n", sep = ""))
  cat(paste("Adj. R-Squared: ", signif(x$r.squared[2], digits), 
            "\n", sep = ""))
  # add the new r squared terms here
  cat(paste("Overall R-Squared:      ", signif(x$r.squared[3], digits), 
            "\n", sep = ""))
  cat(paste("Between R-Squared:      ", signif(x$r.squared[4], digits), 
            "\n", sep = ""))
  fstat <- x$fstatistic
  if (names(fstat$statistic) == "F") {
    cat(paste("F-statistic: ", signif(fstat$statistic), " on ", 
              fstat$parameter["df1"], " and ", fstat$parameter["df2"], 
              " DF, p-value: ", format.pval(fstat$p.value, digits = digits), 
              "\n", sep = ""))
  }
  else {
    cat(paste("Chisq: ", signif(fstat$statistic), " on ", 
              fstat$parameter, " DF, p-value: ", format.pval(fstat$p.value, 
                                                             digits = digits), "\n", sep = ""))
  }
  invisible(x)
}

现在如果我们使用自定义函数：

library(plm)
# Create some random data
set.seed(1) 
x=rnorm(100); fe=rep(rnorm(10),each=10); id=rep(1:10,each=10); ti=rep(1:10,10); e=rnorm(100)
y=x+fe+e

data=data.frame(y,x,id,ti)

# Get plm within R2
reg=plm(y~x,model="within",index=c("id","ti"), effect = "twoways", data=data)

summary.plm.full(reg)

哪些打印：

Twoways effects Within Model

Call:
plm(formula = y ~ x, data = data, effect = "twoways", model = "within", 
    index = c("id", "ti"))

Balanced Panel: n = 10, T = 10, N = 100

Residuals:
    Min.  1st Qu.   Median  3rd Qu.     Max. 
-2.36060 -0.56664 -0.11085  0.56070  2.00869 

Coefficients:
  Estimate Std. Error t-value  Pr(>|t|)    
x  1.12765    0.11306  9.9741 1.086e-15 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Total Sum of Squares:    157.21
Residual Sum of Squares: 70.071
R-Squared:      0.55428
Adj. R-Squared: 0.44842
Overall R-Squared:      0.33672
Between R-Squared:      0.17445
F-statistic: 99.4829 on 1 and 80 DF, p-value: 1.0856e-15