# How to model predicted proportion data without weights

Research Question

I am trying to determine if maternal nest-site choice influences offspring sex ratio in a species where nest temperature determines sex.

Data

I have temperature traces from real nest sites and random sites at six nesting locations. The data was collected over five years. From these temperature traces, I have calculated a predicted sex ratio for each nest and random site. The sex ratio data is continuous, bounded by 0 and 1, with a large number of zeros and ones. Here is a histogram of the data:

I'd like to know if sex ratios vary between nests and random sites, and if this relationship varies between locations.

Analysis Options

Normally, when analysing sex ratio data, I would use a glmm with the binomial or betabinomial error distribution and the number of sexed individuals as the weight term. However, I can't do that in this case because the sex ratios are predicted values, not associated with any real individuals. I have considered three options to solve this issue.

1. Use my predicted sex ratios to generate a number of "fake" individuals for each nest/random site and then use that number as the weights for a binomial/betabinomial glmm. This seems a little too hacky.

2. Use a zero-one inflated beta model (ZOIB). Based on my reading, ZOIB models are appropriate when zero or one values originate from a different underlying process than intermediate values (sources:1,2,3). I don't think this is the case with my data (the difference between a sex ratio of 0 and 0.1 is biologically the same as the difference between a sex ratio of 0.1 and 0.2), although maybe the fact that there are a wider range of temperatures that produce 0 or 1 sex ratios means these results should be treated differently to intermediate values.

3. Use ordered beta regression. Robert Kubenic's method for analysing continuous proportions seems like it might be appropriate for my data (source: 2). I trialed it using the "ordbeta" family in glmmTMB (the model was: Sex Ratio ~ Location*SiteType + (1|year), family=ordbeta), however I don't think the error distribution of my data matches the ordbeta error distribution. My residual plots (made in DHARMa) suggest that the residual error isn't uniform.

Further inspection suggests that there is variation in residual error between the locations:

I used performance::check_predictions to compare model predicted and real values. It seems like there is greater prediction error around zero and one than intermediate values.

I'm wondering if ordered beta regression is the best approach to analysing my data, or if I should try a different solution? If ordered beta regression is the right way to go, what should I do about the error variance issues?

-Thanks

Sources:

• Could you explain the sense in which a sex ratio -- which sounds like one count divided by another -- should be considered "continuous"? What are you counting, what is this a ratio of, and what are typical values of those counts? Since you describe this as "predicted," then in what sense does that help you assess its relationship with temperature?
– whuber
Commented Mar 1 at 20:28
• Are you only comparing the model predicted sex ratio between actual nesting sites and randomly selected sites, or are you comparing observed sex ratios of baby birds born in those nests to the model predicted sex ratios? Commented Mar 1 at 20:30
• @whuber My data is an expected sex ratio rather than a real sex ratio. I used an equation that describes the relationship between sex and temperature for our study species and predicted the chance of developing as a male at the recorded temperatures (0 = no chance to be male, 1= 100% chance of being male). Any value between 0 and 1 is possible, so I don't think I can model it as a discrete varaible, though I should have described it as a probability, not a ratio, sorry! With real sex data you would divide the number of males by the number of females to get the sex ratio. Commented Mar 1 at 20:54
• @whuber I'm not actually looking at the relationship between sex and temperature. I'm testing whether the maternally selected sites would produce different sex ratios than the random sites. Commented Mar 1 at 20:56
• @gung-ReinstateMonica, I'm only comparing the model predicted sex ratios, as we don't have true sex ratio data for many of the nests (for turtles juvenile sex can't be determined without euthanizing hatchlings). Commented Mar 1 at 21:01