I am having a little trouble coming up with a way of analyzing my data. If there is a short answer (i.e., "use logistic regression, dummy") you can just post that and I'll do some digging on my own - I just need to be pointed in the right direction...
My independent variable is a count and my dependent variable is a ratio. Here is the data:
success <- c(322,358,323,277) total.trials <- c(540,533,507,540) count = c(23,13,21,39) ratio <- success/total.trials
IIRC, It's wrong to do a simple linear regression of ratio ~ count... so what method should I utilize here? Thanks for the help.
Okay, so here's some of the code I ran after following gung's advice of employing the use of the GEE:
subject <- c(1, 2, 3, 4) success <- c(322, 358, 323, 277) total <- c(540, 533, 507, 540) count <- c(23, 13, 21, 39) data <- cbind(success,total) gee.model <- gee(data ~ count, id = subject, family = 'binomial') summary(gee.model) GEE: GENERALIZED LINEAR MODELS FOR DEPENDENT DATA gee S-function, version 4.13 modified 98/01/27 (1998) Model: Link: Logit Variance to Mean Relation: Binomial Correlation Structure: Independent Call: gee(formula = data ~ count, id = subject, family = "binomial") Summary of Residuals: Min 1Q Median 3Q Max 276.6608 310.3817 322.1195 331.3620 357.5969 Coefficients: Estimate Naive S.E. Naive z Robust S.E. Robust z (Intercept) -0.25516680 0.031437649 -8.116599 0.0134033383 -19.03756 count -0.01055972 0.001244121 -8.487698 0.0002616798 -40.35360 Estimated Scale Parameter: 0.1066564 Number of Iterations: 1 Working Correlation [,1] [1,] 1
Does this look correct? And, if I am interpreting it correctly, there is a significant effect of count on the proportion.