I have a question concerning the statistical validity of methods. I have data about the survival probabilities of vegetative and reproductive structures of a plant along the flowering time. I am trying to model the survival probability of these structures between the different sexes (females, males), types (flowers and cladodes), and treatments (control and exclusion treatment). The response variable was binomial, 1= alive, and 0= death. I did two methods to analyze this data, but I don't know if it is statistically acceptable.
First, I performed a generalized linear mixed model (GLMM) with binomial error distribution with "probit" link function to estimate the survival probability of flowers between sexes, treatments and types. Using the next model:
m.a <- glmmTMB(survival ~ sex * treatment *type +(1|ID),family=binomial(link="probit"),data=df)
With this model, I used the same data for sex, treatments, and types to PREDICT the probabilities of each row of data used:
dPred <- data.frame(ID = df$ID, sex= df$sex, treatment = df$treatment, type = df$type)
then I used the new data to predict the probabilities of each row used in binomial model:
df.pred<- cbind(dPred, predicted = predict(m.a, type="response", newdata=dPred))
Then, I performed a Linear Mixed-Effects Model using these predicted data. I used the nlme package to fit the model:
model<- lme(predicted ~ sex * treatment *type, random= ~1|ID, data = df.pred)
I performed pairwise comparisons among the different independent variables using emmeans package. My questions are:
Are these methods valid to infer the survival probabilities of these structures? Is there a problem to use these new predicted data to fit this model and to make inferences about the differences among sexes, treatments, and types of structures?
Thank you All the best