Table 3. Regression model specifications.
| Model | Equation | Model specifications |
|---|---|---|
| 1A | xt = β0 + β1t + β2TS1 + β3TS2 + β4TS3 + β5TS4 + β6TS5 + et | xt is the un-aggregated value of WQ parameter which occurred in t-week; yt is the cumulative diarrheal disease count for t-week. |
| 1B | yt = exp{β0 + β1t + β2TS1 + β3TS2 + β4TS3 + β5TS4 + β6TS5 + et} | TS1 through TS5 are binary variables for Tamil season (Table 2); β1 regression coefficient reflects the trend over the study period; β2 through β6 reflect the change in the study parameter as compared to the season-specific reference category (TS6). |
| 2A | xt = β0 + β1t + βLS + et | xt is the un-aggregated value of WQ parameter which occurred in t- week; yt is the cumulative diarrheal disease count for t-week. |
| 2B | yt = exp{β0 + β1t + βLS + et} | β1 regression coefficient reflects the trend and βL (β2 through β5) is the vector of coefficients for a seasonal pattern (S) represented by two harmonics#; a period ω = 365.25 is used to adjust for the effect of a leap year. |
| 3A | xt = β0 + β1t + βLS + β6 Temp + β7Rain + et | xt is the value of un-aggregated WQ parameter which occurred in t-week; yt is the cumulative diarrheal disease count for t-week. |
| 3B | yt = exp{β0 + β1t + βLS + β6 Temp + β7Rain + et} | Interpretation of β1 and βLis similar to Model 2; β6 and β7are effects of weekly average temperature and weekly cumulative rainfall (log10 transformed). |
| 4 | yt = exp{β0 + β1t + βLS + β6 Temp + β7Rain + β8pH + β9NO3− + β10TDS + β11TC + β12FC + et} | yt is the cumulative diarrheal disease count for t-week. |
| Interpretation of β1, βL, β6 and β7are similar to Model 3; β8 through β12are effects of private domain weekly median water quality parameters (TC and FC were log10 transformed). |
#βL is equivalent to β2 sin (2πωt) + β3 cos (2πωt) + β4 sin (4πωt) + β5 cos (4πωt).