Incorrect confidence intervals for precision components of a betareg model

[larmarange]

Please see below an example of a beta regression.

For batch terms, the confidence intervals for the "precision" component are incorrect. These are the confidence intervals for the same terms but for the "mean" component.

library(broom)
library(betareg)
data("GasolineYield", package = "betareg")
mod <- betareg(yield ~ batch + temp | batch + temp, data = GasolineYield)
tidy(mod, conf.int = TRUE) |> 
  knitr::kable()

component	term	estimate	std.error	statistic	p.value	conf.low	conf.high
mean	(Intercept)	-6.4978463	0.0846003	-76.806422	0.0000000	-6.6636598	-6.3320327
mean	batch1	1.5845437	0.0693063	22.862902	0.0000000	1.4487058	1.7203816
mean	batch2	1.4210111	0.0606595	23.426017	0.0000000	1.3021206	1.5399016
mean	batch3	1.6952506	0.0629593	26.926119	0.0000000	1.5718526	1.8186486
mean	batch4	1.0409118	0.0658011	15.819070	0.0000000	0.9119441	1.1698795
mean	batch5	1.2365840	0.0617598	20.022463	0.0000000	1.1155369	1.3576310
mean	batch6	1.0470222	0.0669180	15.646357	0.0000000	0.9158655	1.1781790
mean	batch7	0.6726930	0.0597658	11.255480	0.0000000	0.5555542	0.7898319
mean	batch8	0.5554868	0.0612682	9.066477	0.0000000	0.4354033	0.6755703
mean	batch9	0.3467604	0.0674377	5.141935	0.0000003	0.2145849	0.4789359
mean	temp	0.0117051	0.0001428	81.996405	0.0000000	0.0114253	0.0119849
precision	(Intercept)	-8.7368235	1.7853220	-4.893696	0.0000010	-6.6636598	-6.3320327
precision	batch1	1.4047744	1.1103500	1.265164	0.2058127	1.4487058	1.7203816
precision	batch2	9.0623365	1.2376412	7.322265	0.0000000	1.3021206	1.5399016
precision	batch3	5.6579558	1.2430910	4.551522	0.0000053	1.5718526	1.8186486
precision	batch4	1.8084883	1.0910103	1.657627	0.0973928	0.9119441	1.1698795
precision	batch5	3.3999312	1.1600801	2.930773	0.0033812	1.1155369	1.3576310
precision	batch6	1.9603814	1.1579044	1.693043	0.0904474	0.9158655	1.1781790
precision	batch7	5.5540694	1.1127723	4.991200	0.0000006	0.5555542	0.7898319
precision	batch8	2.0602136	1.1497873	1.791821	0.0731616	0.4354033	0.6755703
precision	batch9	1.3619734	1.2872171	1.058076	0.2900208	0.2145849	0.4789359
precision	temp	0.0376697	0.0040708	9.253675	0.0000000	0.0114253	0.0119849

^{Created on 2023-08-07 with reprex v2.0.2}

[simonpcouch]

Thank you for the report!

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