如何使用R进行逻辑回归，测试有序分类变量中线性趋势的偏离？

Question

I'm testing for a linear trend in the log odds of a binary outcome across an ordered categorical independent variable. This is straightforwardly achieved by treating the independent variable as continuous.

I'm also trying to test for departure from linear trend. I understand that this is about comparing (a) the model where the independent variable is categorical with (b) the model where the independent variable is treated as continuous. But I'm not sure how to do this in R.

Can anyone help?

I've created a reproducible example below. The first 7 lines just create a dataset. model1 treats the independent variable as categorical; model2 as continuous.

model2 provides strong evidence that a linear trend explains the trend better than no trend at all, but a linear trend is clearly not a very good explanation in this case.

# create dataset 'a'

n <- 200
ngroups <- 7
a <- data.frame(group = rep(letters[1:ngroups], n), group2 = rep(1: ngroups, n), n = runif(n * ngroups, 0, 1))
y <- data.frame(group = letters[1:ngroups], fac = 1/(1 + exp(-1 * 1:ngroups)))
a <- merge(a, y, by = "group")
a$n2 <- a$n * a$fac
a$ind <- ifelse(a$n2 > quantile(a$n2)[4], 1, 0)

# run models

model1 <- glm(ind ~ group, data = a, family = "quasibinomial")
model2 <- glm(ind ~ group2, data = a, family = "quasibinomial") 

Answer 1

Answering my own question...

You do a likelihood ratio test to compare the two models:

anova(model1, model2, test = "LRT")

This is likely to give a low p-value, suggesting that the models are different, and there is evidence that a non-linear trend fits the data better than a linear trend.