# High frequency zero-inflated negative binomial model with Hauck-Donner effect

I have high-frequency (daily) data with overdispersion and a high amount of zeros. I know that a zero-inflated negative binomial is my best option for a model. I am using the library ZIM in R. By using it I'm also correcting for autocorrelation given the high frequency of my data. This is my data where admissions has 281 0s out of 1304.

str(data)
'data.frame':   1304 obs. of  14 variables:
$date : POSIXct, format: "2016-06-05" "2016-06-06" "2016-06-07" ...$ PM2.5        : num  9.91 9.81 8.54 9.91 11.36 ...
$Admissions : int 1 4 5 10 13 8 3 5 13 9 ...$ no2      : num  3.05 2.86 2.62 3.68 5.95 ...

I'm trying to explain the number of ER admissions Admissions given the day's level of no2 or PM2.5. For both options, I get gigantic standard errors in my solution.

To run ZIM I calculate lags for both my dependent Admissions and independent variable no2.

countT<-data$Admissions>0 trend <- 1:length(countT) / 1000 lag<-dplyr::lag(data$no2, n = 30)
ar<-bshift(countT, k=11)

This is my output

Call:
zim(formula = countT ~ ar + data$$no2 + lag + trend | data$$no2 + lag + trend, dist = "zinb")

Coefficients (log-linear):
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.2627172  0.1356004 -9.3120   <2e-16 ***
ar           1.1094678  0.1139324  9.7379   <2e-16 ***
data$$no2 0.0019484 0.0064083 0.3040 0.7611 lag 0.0039566 0.0063934 0.6189 0.5360 trend 0.0265951 0.0835536 0.3183 0.7503 Coefficients (logistic): Estimate Std. Error z value Pr(>|z|) (Intercept) -19.29889 1744.68667 -0.0111 0.9912 data$$no2       0.15399  106.47153  0.0014   0.9988
lag           -0.30275  252.52797 -0.0012   0.9990
trend          0.15710 1349.33740  0.0001   0.9999
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for negative binomial taken to be 78934295.4758)

Criteria for assessing goodness of fit
loglik: -1154.959
aic: 2329.917
bic: 2381.266
tic: 2312.124

Number of EM-NR iterations: 19