檢查有序邏輯回歸中的平行回歸假設

Question

我嘗試使用一個有序分類變量和另外三個分類因變量（N = 43097）構建有序邏輯回歸。 雖然所有系數都很重要，但我對是否滿足平行回歸假設表示懷疑。 盡管brant test中所有變量和整個模型的概率值完全為零（應該大於 0.05），但測試仍然顯示H0: Parallel Regression Assumption holds 。 我在這里很困惑。 這個模型是否完全符合平行回歸假設的標准？

library(MASS)
table(hh18_u_r$cat_ci_score) # Dependent variable

Extremely Vulnerable  Moderate Vulnerable    Pandemic Prepared 
              6143                16341                20613 

# Ordinal logistic regression
olr_2 <- polr(cat_ci_score ~ r1_gender + r2_merginalised + r9_religion, data = hh18_u_r, Hess=TRUE)
summary(olr_2)

Call:
polr(formula = cat_ci_score ~ r1_gender + r2_merginalised + r9_religion, 
  data = hh18_u_r, Hess = TRUE)

Coefficients:
                      Value Std. Error t value
r1_genderMale          0.3983    0.02607  15.278
r2_merginalisedOthers  0.6641    0.01953  34.014
r9_religionHinduism   -0.2432    0.03069  -7.926
r9_religionIslam      -0.5425    0.03727 -14.556

Intercepts:
                                       Value    Std. Error t value 
Extremely Vulnerable|Moderate Vulnerable  -1.5142   0.0368   -41.1598
Moderate Vulnerable|Pandemic Prepared      0.4170   0.0359    11.6260

Residual Deviance: 84438.43 
AIC: 84450.43 

## significance of coefficients and intercepts
summary_table_2 <- coef(summary(olr_2))
pval_2 <- pnorm(abs(summary_table_2[, "t value"]), lower.tail = FALSE)* 2
summary_table_2 <- cbind(summary_table_2, pval_2)
summary_table_2

                                            Value Std. Error    t value        pval_2
r1_genderMale                             0.3982719 0.02606904  15.277583  1.481954e-52
r2_merginalisedOthers                     0.6641311 0.01952501  34.014386 2.848250e-250
r9_religionHinduism                      -0.2432085 0.03068613  -7.925682  2.323144e-15
r9_religionIslam                         -0.5424992 0.03726868 -14.556436  6.908533e-48
Extremely Vulnerable|Moderate Vulnerable -1.5141502 0.03678710 -41.159819  0.000000e+00
Moderate Vulnerable|Pandemic Prepared     0.4169645 0.03586470  11.626042  3.382922e-31

#Test of parallel regression assumption
library(brant)
brant(olr_2) # Probability supposed to be more than 0.05 as I understand

---------------------------------------------------- 
Test for        X2  df  probability 
---------------------------------------------------- 
Omnibus         168.91  4   0
r1_genderMale       12.99   1   0
r2_merginalisedOthers   41.18   1   0
r9_religionHinduism 86.16   1   0
r9_religionIslam    25.13   1   0
---------------------------------------------------- 

H0: Parallel Regression Assumption holds

# Similar test of parallel regression assumption using car package
library(car)
car::poTest(olr_2)
Tests for Proportional Odds
polr(formula = cat_ci_score ~ r1_gender + r2_merginalised + r9_religion, 
  data = hh18_u_r, Hess = TRUE)

                    b[polr] b[>Extremely Vulnerable] b[>Moderate Vulnerable] Chisquare df Pr(>Chisq)    
Overall                                                                            168.9  4    < 2e-16 ***
r1_genderMale           0.398                    0.305                   0.442      13.0  1    0.00031 ***
r2_merginalisedOthers   0.664                    0.513                   0.700      41.2  1    1.4e-10 ***
r9_religionHinduism    -0.243                   -0.662                  -0.147      86.2  1    < 2e-16 ***
r9_religionIslam       -0.542                   -0.822                  -0.504      25.1  1    5.4e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

請建議這個模型是否滿足平行回歸假設？ 謝謝

Answer 1

它告訴您零假設 (H0) 成立。 您的值具有統計顯着性，這意味着您拒絕原假設 (H0)。 它並沒有向您表明滿足假設，而只是提醒您什么是空值。