R &引用；不适用；当我试图建立一个三因素相互作用的模型时，在我的回归输出中突然出现

我首先创建我的数据集：

ExperimentDesign <- expand.grid(A = gl(2, 1, labels = c("-", "+")),
                                B = gl(2, 1, labels = c("-", "+")),
                                C = gl(2, 1, labels = c("-", "+")))

ExperimentDesign$response <- c(266.4,270.8,240.8,245.6,280.6,277.2,285.8,280.6)

我做回归分析：

model <- lm(response ~ A + B + C + A*B + A*C + B*C + A*B*C, 
                  
                data = ExperimentDesign)

summary(model)

当我将模型更改为此时：

model <- lm(response ~ A + B + C + A*B + A*C + B*C, 
                  
                data = ExperimentDesign)

summary(model)

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关于我不使用三因素交互建模时模型运行良好的原因，以及如何让它使用三因素交互正确运行模型的任何见解？

因为您没有三因素组合的复制，当你估计每个组合的平均值时，你已经用完了你所有的自由度（例如，进行三方交互）。您有8行数据，并花费8个df。请注意输出中的

0自由度

。

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)    266.4         NA      NA       NA
A+               4.4         NA      NA       NA
B+             -25.6         NA      NA       NA
C+              14.2         NA      NA       NA
A+:B+            0.4         NA      NA       NA
A+:C+           -7.8         NA      NA       NA
B+:C+           30.8         NA      NA       NA
A+:B+:C+        -2.2         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom
Multiple R-squared:      1, Adjusted R-squared:    NaN 
F-statistic:   NaN on 7 and 0 DF,  p-value: NA

model <- lm(response ~ A + B + C + A*B + A*C + B*C, 
                  
                data = ExperimentDesign)

summary(model)

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept) 266.1250     0.7276 365.767  0.00174 **
A+            4.9500     0.9526   5.196  0.12104   
B+          -25.0500     0.9526 -26.296  0.02420 * 
C+           14.7500     0.9526  15.483  0.04106 * 
A+:B+        -0.7000     1.1000  -0.636  0.63921   
A+:C+        -8.9000     1.1000  -8.091  0.07829 . 
B+:C+        29.7000     1.1000  27.000  0.02357 * 
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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1