Question

是否可以从包lmtest中的grangertest输出计算效果大小？我可以手工计算它，但它只给出F值，而不是平方和。

Granger causality test

Model 1: apwbc ~ Lags(apwbc, 1:1) + Lags(other, 1:1)
Model 2: apwbc ~ Lags(apwbc, 1:1)
  Res.Df Df      F  Pr(>F)  
1    163                    
2    164 -1 4.8495 0.02906 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Answer 1

我们说变量 X Granger导致变量 Y 如果基于 X 的滞后值 Y 的预测 Y 的滞后值，em>和 Y 明显优于 Y 的预测。这意味着格兰杰因果关系检验是对嵌套模型的检验;具有两个变量滞后的模型是完整模型，并且仅具有滞后 Y 的模型是嵌套或受限模型。我们可以通过嵌套模型的测试计算部分η²为（ SS _restricted - SS _full ）/ SS _restricted （参见例如Wright and London (2009)，第21页）。

这很容易编码：

nested_model_partial_eta_sq <- function(full_mod, rest_mod) {
    # full_mod is the full model (an lm object)
    # rest_mod is the model that omits one or more explanatory variables
    SS_full <- sum(full_mod$residuals^2)
    SS_rest <- sum(rest_mod$residuals^2)
    return((SS_rest - SS_full) / SS_rest)
}

但是，我们可能还需要一个为我们生成回归的函数，以及运行Granger因果关系检验：

custom_granger <- function(x, y, p = 1) {
    # Does x Granger cause y? What is the effect size?
    # We want to test Granger causality,
    # but then also get partial eta squared to measure effect size
    # First it will be convenient to store the variable names
    varnames <- c(deparse(substitute(x)), deparse(substitute(y)))
    lagnames <- paste0(varnames, "_lag", rep(1:p, each = 2))
    # Then we created the lagged variables / data for models
    VAR_data <- embed(as.matrix(cbind(x, y)), p + 1)
    colnames(VAR_data) <- c(varnames, lagnames)
    VAR_data <- VAR_data[, -1]
    # Run the full model
    model_formula <- paste(colnames(VAR_data)[-1], collapse = " + ")
    model_formula <- formula(paste0(varnames[2], " ~ ", model_formula))
    full_mod <- lm(model_formula, data = as.data.frame(VAR_data))
    # Take out the lags of x and run the nested model
    VAR_data <- VAR_data[ , seq(from = 1, to = p * 2 + 1, by = 2)]
    model_formula <- paste(colnames(VAR_data)[-1], collapse = " + ")
    model_formula <- formula(paste0(varnames[2], " ~ ", model_formula))
    rest_mod <- lm(model_formula, data = as.data.frame(VAR_data))
    # Then we can do the Granger test
    granger_test <- anova(full_mod, rest_mod)
    # and get partial eta squared
    SS_full <- granger_test$RSS[1]
    SS_rest <- granger_test$RSS[2]
    partial_eta_squared <- (SS_rest - SS_full) / SS_rest
    # And return all of it
    return(list(VAR_result = full_mod,
                granger_test = granger_test,
                partial_eta_squared = partial_eta_squared))
}

使用您的数据会产生

df <- read.csv('cormanaz-data.txt')
with(df, custom_granger(other, apwbc))

$VAR_result

Call:
lm(formula = model_formula, data = as.data.frame(VAR_data))

Coefficients:
(Intercept)   other_lag1   apwbc_lag1  
    1.97732     -0.01671      0.48997  


$granger_test
Analysis of Variance Table

Model 1: apwbc ~ other_lag1 + apwbc_lag1
Model 2: apwbc ~ apwbc_lag1
  Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
1    163 6267.9                              
2    164 6454.4 -1   -186.48 4.8495 0.02906 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

$partial_eta_squared
[1] 0.02889191

您可以看到Granger因果关系检验的 F 统计量与lmtest::grangertest()相同，但这也会给出VAR系数和部分η^{2 < / sup>，对于你的特定情况（我猜你一直以来的数字）约为0.029。}

r lmtest格兰杰因果关系的影响大小？

1 个答案: