当不使用截距时Java中线性模型的Anova与R中的Anova不同

Question

这是我在这里提出的问题之后的一个后续问题：Is there an equivalent function for anova.lm() in Java?。在这些答案的帮助下，我可以在Java中得到与R中相同的结果，当对两个线性模型进行截取时，结果是相同的。然而，当我从线性模型中删除截距时，残差平方和是相同的，但Java和R中的p值是不同的。

在删除拦截时，是否应该以不同的方式计算FDistribution？

R码

test_trait <- c( -0.48812477 , 0.33458213, -0.52754476, -0.79863471, -0.68544309, -0.12970239,  0.02355622, -0.31890850,0.34725819 , 0.08108851)
geno_A <- c(1, 0, 1, 2, 0, 0, 1, 0, 1, 0)
geno_B <- c(0, 0, 0, 1, 1, 0, 0, 0, 0, 0) 

fit <- lm(test_trait ~ geno_A+geno_B)
fit2 <- lm(test_trait ~ geno_A + geno_B + geno_A:geno_B)
anova(fit, fit2)
#   Res.Df     RSS Df Sum of Sq      F Pr(>F)
# 1      7 0.77982                           
# 2      6 0.77053  1 0.0092897 0.0723  0.797

fit <- lm(test_trait ~ geno_A+geno_B -1 )
fit2 <- lm(test_trait ~ geno_A + geno_B + geno_A:geno_B-1)
anova(fit, fit2)
#   Res.Df     RSS Df Sum of Sq      F Pr(>F)
# 1      8 0.78539                           
# 2      7 0.77080  1  0.014593 0.1325 0.7266

Java

double[] y =  {-0.48812477, 0.33458213, -0.52754476, -0.79863471, -0.68544309, -0.12970239, 0.02355622, -0.31890850, 0.34725819,  0.08108851};
double[][] x = {{1,0}, {0,0}, {1,0}, {2,1}, {0,1}, {0,0}, {1,0}, {0,0}, {1,0}, {0,0}};
double[][] xb = {{1,0,0}, {0,0,0}, {1,0,0}, {2,1,2}, {0,1,0}, {0,0,0}, {1,0,0}, {0,0,0}, {1,0,0}, {0,0,0}};
OLSMultipleLinearRegression regr = new OLSMultipleLinearRegression();
regr.newSampleData(y, x);
double sumOfSquaresModelA = regr.calculateResidualSumOfSquares();
regr.newSampleData(y, xb);
double sumOfSquaresModelB = regr.calculateResidualSumOfSquares();
int degreesOfFreedomA = y.length - (x[0].length + 1);
int degreesOfFreedomB = y.length - (xb[0].length + 1);
double MSE = sumOfSquaresModelB / degreesOfFreedomB; 
System.out.printf("RSS intercept: %f\n",sumOfSquaresModelB);
int degreesOfFreedomDifference = Math.abs(degreesOfFreedomB - degreesOfFreedomA);
double MSEdiff = Math.abs((sumOfSquaresModelB - sumOfSquaresModelA) / (degreesOfFreedomDifference));
double Fval = MSEdiff / MSE;
FDistribution Fdist = new FDistribution(degreesOfFreedomDifference, degreesOfFreedomB);
double pval = 1 - Fdist.cumulative(Fval);
System.out.printf("pval with intercept: %f\n",pval);
regr.setNoIntercept(true);
regr.newSampleData(y, x);
double sumOfSquaresNoInterceptA = regr.calculateResidualSumOfSquares();
regr.newSampleData(y, xb);
double sumOfSquaresNoInterceptB = regr.calculateResidualSumOfSquares();
MSE = sumOfSquaresNoInterceptB / degreesOfFreedomB;
System.out.printf("RSS no intercept: %f\n",sumOfSquaresNoInterceptB);
degreesOfFreedomDifference = Math.abs(degreesOfFreedomB - degreesOfFreedomA);
MSEdiff = Math.abs((sumOfSquaresNoInterceptB - sumOfSquaresNoInterceptA) / (degreesOfFreedomDifference));
Fval = MSEdiff / MSE;
Fdist = new FDistribution(degreesOfFreedomDifference, degreesOfFreedomB);
pval = 1 - Fdist.cumulative(Fval);
System.out.printf("pval without intercept: %f",pval);

结果

RSS intercept: 0.770528              //correct
pval with intercept: 0.796973        //correct
RSS no intercept: 0.770799           //correct
pval without intercept: 0.747564     //wrong

Answer 1

删除拦截增加了额外的自由度，而我并没有将其包含在Java代码中。下面给出了相同的结果

double[] y =  {-0.48812477, 0.33458213, -0.52754476, -0.79863471, -0.68544309,  -0.12970239, 0.02355622, -0.31890850, 0.34725819,  0.08108851};
double[][] x = {{1,0}, {0,0}, {1,0}, {2,1}, {0,1}, {0,0}, {1,0}, {0,0}, {1,0}, {0,0}};
double[][] xb = {{1,0,0}, {0,0,0}, {1,0,0}, {2,1,2}, {0,1,0}, {0,0,0}, {1,0,0}, {0,0,0}, {1,0,0}, {0,0,0}};
OLSMultipleLinearRegression regr = new OLSMultipleLinearRegression();
int degreesOfFreedomA = y.length - (x[0].length); // no + 1
int degreesOfFreedomB = y.length - (xb[0].length); // no + 1
regr.setNoIntercept(true);
regr.newSampleData(y, x);
double sumOfSquaresNoInterceptA = regr.calculateResidualSumOfSquares();
regr.newSampleData(y, xb);
double sumOfSquaresNoInterceptB = regr.calculateResidualSumOfSquares();
double MSE = sumOfSquaresNoInterceptB / degreesOfFreedomB;
System.out.printf("RSS no intercept: %f\n",sumOfSquaresNoInterceptB);
int degreesOfFreedomDifference = Math.abs(degreesOfFreedomB - degreesOfFreedomA);
double MSEdiff = Math.abs((sumOfSquaresNoInterceptB - sumOfSquaresNoInterceptA) / (degreesOfFreedomDifference));
double Fval = MSEdiff / MSE;
FDistribution Fdist = new FDistribution(degreesOfFreedomDifference, degreesOfFreedomB);
double pval = 1 - Fdist.cumulative(Fval);
System.out.printf("pval without intercept: %f",pval);

结果

pval without intercept: 0.726572