检查有序逻辑回归中的平行回归假设

Question

I have tried to build an ordinal logistic regression using one ordered categorical variable and another three categorical dependent variables (N= 43097). While all coefficients are significant, I have doubts about meeting the parallel regression assumption. Though the probability values of all variables and the whole model in the brant test are perfectly zero (which supposed to be more than 0.05), still test is displaying that H0: Parallel Regression Assumption holds . I am confused here. Is this model perfectly meets the criteria of the parallel regression assumption?

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

Kindly suggest whether this model satisfies the parallel regression assumption? Thank you

Answer 1

It tells you the null hypothesis (H0) is that it holds. Your values are statistically significant, which means you reject the null hypothesis (H0). It wasn't showing you that to say the assumption was met but rather it was just a reminder of what the null is.