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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'.

Jackk
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  • Can you provide more details on capfactor? – Isabella Ghement Jul 12 '19 at 16:21
  • What kind of details do you need? It is a variable ranging between 0 and 1 – Jackk Jul 12 '19 at 19:34
  • Is it a variable computed as "number of successes out of n trials", where n is known in advance? – Isabella Ghement Jul 12 '19 at 23:03
  • No, it is a physical index ranging between 0 and 1. – Jackk Jul 13 '19 at 08:11
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    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. – Isabella Ghement Jul 13 '19 at 13:42
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    See this post, for example, about ‘continuous’ proportions and how to model them: http://support.sas.com/kb/57/480.html. In principle, you could use beta-regression modelling (which can accommodate zero- and/or one- inflation). – Isabella Ghement Jul 13 '19 at 13:44
  • This post may be useful too: http://www.petrkeil.com/?p=603. – Isabella Ghement Jul 13 '19 at 13:46
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    For ‘discrete’ proportions modeled via binomial regression, this post should help: https://www.theanalysisfactor.com/when-to-use-logistic-regression-for-percentages-and-counts/. – Isabella Ghement Jul 13 '19 at 13:48

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