get_predicted(): zero-inflation options

[bwiernik]

Currently, for zero-inflated models, get_predicted() and its downstream functions like modelbased::estimate_expectation() always return the equivalent to type = "conditional" (predicted values assuming non-zero). It would be good to allow users to specify other methods, such as predicting unconditional response predictions (incorporating both parts of the model) or just the zero-inflation parts.

It would also be good I think to make the default equivalent to type = "response" (incorporating both model parts).

See the type argument in predict.glmmTMB():

type
Denoting mu as the mean of the conditional distribution and p as the zero-inflation probability, the possible choices are:

"link"
conditional mean on the scale of the link function, or equivalently the linear predictor of the conditional model
"response"
expected value; this is mu*(1-p) for zero-inflated models and mu otherwise
"conditional"
mean of the conditional response; mu for all models (i.e., synonymous with "response" in the absence of zero-inflation
"zprob"
the probability of a structural zero (gives an error for non-zero-inflated models)
"zlink"
predicted zero-inflation probability on the scale of the logit link functio>
"disp"
dispersion parameter however it is defined for that particular family as described in sigma.glmmTMB

[DominiqueMakowski]

do you have a reproducible example with a model that has these components so I can play around?

[bwiernik]

Away from computer. The second example in ?glmmTMB

[DominiqueMakowski]

library(glmmTMB)

m <- glmmTMB(count ~ spp + mined + (1|site),
             zi=~spp + mined,
             family=nbinom2, data=Salamanders)


head(insight::get_predicted(m))
#> [1] 0.5387752 1.0768783 0.3554236 2.4701755 2.4950498 2.1819828
head(insight::get_predicted(m, type = "zprob"))
#> [1] 2.040119 2.040119 2.040119 1.174339 1.174339 1.174339

^{Created on 2021-08-04 by the reprex package (v2.0.0)}

custom types should work after the latest commit.

So now it becomes a question or wether we want to change / add to the behaviour of our main predict argument (this is also what would drive easystats/modelbased#136). We could have predict = "dispersion" or something like that, but then again I'm not very familiar with these models so I don't know

[bwiernik]

Yes, I think the predict argument should have options for zero inflated and dispersion parameters

[bwiernik]

I think we should revert the type argument. Our predict argument fills the same role, and it's confusing to have two.

Instead, I think we add options to predict to include these:

Existing

• "link"
  • linear predictor on the link scale (the conditional part for zero-inflated models)
  • with confidence intervals (uncertainty intervals on linear prediction)
  • same as glmmTMB's type = "link"

Existing labels, need adjusted behavior

• "expectation"
  • expected value (mean) on the response scale, including both the zero-inflated and conditional parts
  • with confidence intervals (uncertainty intervals on the conditional mean)
  • currently, it ignores the zero-inflated part
  • should be mu*(1-p) for zero-inflated models and mu otherwise
  • This would be equivalent to glmmTMB's type = "response"
• "prediction"
  • expected value (mean) on the response scale, including both the zero-inflated and conditional parts
  • with predction intervals (uncertainty intervals on the individual cases)
• "response"
  • "prediction", but classifying probabilities in binomial models to 0-1
  • uncertainty intervals would generally become [0, 1] for bernoulli models, but could be a range of integers for binomial models with multiple trials

New labels

• "conditional"
  • expected value (mean) on the response scale, conditional on non-structural zero
  • with confidence intervals (uncertainty intervals on the conditional mean)
  • what is currently returned by predict = "expectation"
• "zprob"
  • expected probability of a structural zero
  • with confidence intervals (uncertainty intervals on the expected probability)
  • effectively the "expectation" for the zero-inflation part of the model
  • should give an error or message for non-zero-inflated models
• "zlink"
  • linear predictor for a structural zero on the link scale
  • with confidence intervals (uncertainty intervals on the linear prediction)
  • effectively the "expectation" for the zero-inflation part of the model
  • should give an error or message for non-zero-inflated models
• "dispersion"
  • expected value for the dispersion parameter for the model (e.g., conditional SD for a normal linear model)
  • with confidence intervals (uncertainty intervals on the conditional dispersion)
  • For gaussian models with type = "disp", glmmTMB returns estimates/CI on the sigma (SD) scale; I don't see a need to offer other scales (variance or log-variance [this is what is actually modeled])

For predict = "prediction", we should include the dispersion parameter in the prediction intervals. @DominiqueMakowski If you could add a placeholder for that, I can fill in the necessary extractions from glmmTMB objects. How do we currently handle dispersion for things like Poisson models where there is a variance term in the model?

[DominiqueMakowski]

The needed steps to add/edit I believe are:

• extending the list of possible arguments here:

insight/R/get_predicted.R

Line 275 in 1540c06

predict = c("expectation", "link", "prediction", "response", "relation"),

• editing the logic here for the type:

insight/R/get_predicted.R

Lines 645 to 652 in 1540c06

	# Type (that's for the initial call to stats::predict)
	if (!is.null(type) && all(type == "auto")) {
	if (info$is_linear) {
	type <- "response"
	} else {
	type <- "link"
	}
	}

• and here for the CI

insight/R/get_predicted.R

Lines 633 to 643 in 1540c06

	# Prediction and CI type
	if (predict == "link") {
	ci_type <- "confidence"
	scale <- "link"
	} else if (predict == "expectation") {
	ci_type <- "confidence"
	scale <- "response"
	} else if (predict %in% c("prediction", "response")) {
	ci_type <- "prediction"
	scale <- "response"
	}

(essentially since we have one "master" argument predict, it is then passed to the .get_predicted_args() helper that assigns the traditional arguments)

[strengejacke]

@DominiqueMakowski can insight be submitted, or is there anything that needs to be addressed for modelbased?

[DominiqueMakowski]

I wouldn't say that this issue of adding more options for glmmTMB is urgent so probably not a blocker for a CRAN update

[strengejacke]

I think this will be closed in #501

[strengejacke]

should be resolved in #501 to #503