TABLE 1.
Results for the data of the nine-year-old children from the Iowa Fluoride Study. We used the Maximum Pseudo Likelihood (MPL) estimators with adjusted sandwich standard error (Adj_SW) and the Modified Expectation-Solution (MES) estimators with a B = 500 size bootstrap standard error (BS). Results from a standard zero-inflated Poisson analysis with a Hessian-based standard error from the pscl package (SE (pscl)) are also shown for comparison.
| ZICMP (MPL) | ||||||
|---|---|---|---|---|---|---|
| Counts | SE (Adj_SW) | P-value | Zero-inflation | SE (Adj_SW) | P-value | |
| Intercept | 1.2571 | 0.4708 | 0.008** | 2.1507 | 0.7839 | 0.006** |
| Gender(Male=1) | −0.0154 | 0.0545 | 0.777 | 0.1363 | 0.1235 | 0.270 |
| DentalExamAge | −0.0360 | 0.0394 | 0.361 | −0.0791 | 0.0795 | 0.320 |
| AUCmhF5_9yrs | 0.0137 | 0.1087 | 0.900 | 0.7741 | 0.2127 | <0.0001** |
| AUCSodaOz5_9yrs | −0.0120 | 0.0116 | 0.302 | −0.0721 | 0.0241 | 0.003** |
| ToothBrushingFeq.Per_DayAvg | −0.1476 | 0.0612 | 0.016* | 0.5607 | 0.1249 | <0.0001** |
| Dental VisitPat6moth Avg | 0.1161 | 0.1522 | 0.446 | −0.5297 | 0.2785 | 0.057 |
| FluorideTreatmentPast6monthAvg | 0.1010 | 0.1264 | 0.424 | −0.0186 | 0.1951 | 0.924 |
| HomeFluorideppm.Avg | −0.1551 | 0.0801 | 0.053 | −0.3179 | 0.1710 | 0.063 |
| v | 0.6027 | 0.1060 | ||||
|
| ||||||
| ZICMP (MES) | ||||||
| Counts | SE (BS) | P-value | Zero-inflation | SE (BS) | P-value | |
| Intercept | 0.9273 | 0.6253 | 0.138 | 2.2401 | 0.8463 | 0.008** |
| Gender(Male=1) | −0.0134 | 0.0548 | 0.807 | 0.1408 | 0.1266 | 0.266 |
| DentalExamAge | −0.0081 | 0.0591 | 0.891 | −0.0884 | 0.0902 | 0.327 |
| AUCmhF5_9yrs | 0.0135 | 0.1136 | 0.905 | 0.7041 | 0.2293 | 0.002** |
| AUCSodaOz5_9yrs | −0.0098 | 0.0119 | 0.409 | −0.0704 | 0.0245 | 0.004** |
| ToothBrushingFeq.Per_DayAvg | −0.1225 | 0.0649 | 0.059 | 0.5664 | 0.1371 | <0.0001** |
| Dental VisitPat6moth Avg | −0.0604 | 0.1745 | 0.729 | −0.4932 | 0.3537 | 0.163 |
| FluorideTreatmentPast6monthAvg | 0.0765 | 0.1228 | 0.533 | −0.0643 | 0.2138 | 0.7636 |
| HomeFluorideppm.Avg | −0.1580 | 0.0854 | 0.064 | −0.2877 | 0.1892 | 0.1283 |
| v | 0.5975 | 0.1362 | ||||
|
| ||||||
| ZIP | ||||||
| Counts | SE (pscl, adj_sw) | P-value(pscl, adj_sw) | Zero-inflation | SE (pscl, adj_sw) | P-value(pscl, adj_sw) | |
| Intercept | 0.5737 | 0.2994, 0.4886 | 0.055, 0.2403 | 2.1560 | 0.4469, 0.7578 | <0.0001**, 0.0044** |
| Gender(Male=1) | −0.0174 | 0.0369, 0.0690 | 0.639, 0.8017 | 0.1540 | 0.0648, 0.1224 | 0.018*, 0.2084 |
| DentalExamAge | 0.0771 | 0.0296, 0.0480 | 0.009**, 0.1080 | −0.0814 | 0.0451, 0.0773 | 0.071, 0.2928 |
| AUCmhF5_9yrs | −0.0185 | 0.0688, 0.1355 | 0.788, 0.8911 | 0.4701 | 0.1129, 0.1963 | <0.0001**, 0.0166* |
| AUCSodaOz5_9yrs | −0.0055 | 0.0075, 0.0146 | 0.466, 0.7073 | −0.0560 | 0.0129, 0.0235 | <0.0001**, 0.0114* |
| ToothBrushingFeq.Per_DayAvg | −0.0745 | 0.0418, 0.0708 | 0.075, 0.2926 | 0.6070 | 0.0697, 0.1221 | <0.0001**, < 0.0001** |
| Dental VisitPat6moth Avg | 0.0962 | 0.1045, 0.1791 | 0.358, 0.5912 | −0.2886 | 0.1678, 0.2862 | 0.085, 0.3133 |
| FluorideTreatmentPast6monthAvg | 0.0029 | 0.0677, 0.1397 | 0.967, 0.9837 | −0.2490 | 0.1135, 0.2055 | 0.028*, 0.2256 |
| HomeFluorideppm.Avg | −0.1863 | 0.0477, 0.0961 | <0.0001**, 0.0525 | −0.1573 | 0.0768, 0.1503 | 0.041*, 0.2952 |
*
0.01 < p-value < 0.05,
**
p-value < 0.01