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
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.