# Interpretation of fractional regression (GLM quasibinomial with logit link) coefficients

I am writing a research paper commenting theresults of the following regression, which is a GLM quasibionomial regression with a logit link (the outcome variable capfactor ranges between 0 and 1).

formula<-capfactor ~  log(input)
myglm1<-glm(formula,data=daily2, family = quasibinomial('logit'))
coeftest(myglm1, vcov.=vcovHC(myglm1, type="HC0"))


Here is the summary of the results:

z test of coefficients:

Estimate Std. Error z value  Pr(>|z|)
(Intercept)               0.976206   0.104157  9.3724 < 2.2e-16 ***
log(input)               -0.067847   0.024697 -2.7472  0.006011 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


I am strugguling to interpret the coefficient in human-understandable terms. I am aware of this answer Logit-link GLM Summary Interpretation, but still I am not able to formulate a satisfactory result statement. How can I derive something like an 'average marginal effect' interpretation from the coefficient?

Something along the lines of:

'On average a 1% increase in the input variable yields to a x percentage points decline in the capfactor variable'.

• Can you provide more details on capfactor? Jul 12, 2019 at 16:21
• What kind of details do you need? It is a variable ranging between 0 and 1 Jul 12, 2019 at 19:34
• There are two kinds of proportions: ‘discrete’ and ‘continuous’. A ‘discrete’ proportion is one that can be expressed as ‘proportion of successes over n trials’ (e.g., proportion of correct answers on a test with 10 questions). A ‘continuous’ proportion is one that cannot be thought of as ‘discrete’, such as your capfactor variable. The model you used is inappropriate for a response variable whose values are ‘continuous’ proportions, so how you interpret its findings becomes irrelevant. The model would only apply if capfactor’s values could be thought of as ‘discrete’ proportions. Jul 13, 2019 at 13:42
• See this post, for example, about ‘continuous’ proportions and how to model them: support.sas.com/kb/57/480.html. In principle, you could use beta-regression modelling (which can accommodate zero- and/or one- inflation). Jul 13, 2019 at 13:44
• For ‘discrete’ proportions modeled via binomial regression, this post should help: theanalysisfactor.com/…. Jul 13, 2019 at 13:48