Table 2.
Summary of power, bias, and precision of parameter estimates and interpretability from 50,000 simulation runs across the six combinations of the dependent variable Y and the predictor X. Each combination was either fitted using a Gaussian error structure or the appropriate error structure according to the distribution of Y (that is either Poisson with a mean of 1 or binomial with a mean of 0.75). The predefined effect was chosen such that a power of around 0.5 was reached (see Table S2 for details). The column Effect is the mean estimated effect (intercept + slope) after back-transformation
| Distribution of Y | Distribution of X | Error distribution | Sample size | Power at α = 0.05 | Power at α = 0.001 | Mean of slope b | Variance in slope b | CV of slope b | Mean intercept a | Variance in intercept a | CV of intercept a | Effect | Variance in effect |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Poisson | Gaussian | Gaussian | 100 | 0.522 | 0.094 | 0.200 | 9.96 × 10-3 | 0.498 | 1.000 | 9.70 × 10-3 | 0.098 | 1.201 | 0.023 |
| Poisson | Gaussian | Poisson | 100 | 0.511 | 0.090 | 1.228 | 0.015 | 0.100 | 0.976 | 9.80 × 10-3 | 0.101 | 1.195 | 0.022 |
| Binomial | Gaussian | Gaussian | 100 | 0.502 | 0.085 | 0.085 | 1.79 × 10-3 | 0.500 | 0.750 | 1.82 × 10-3 | 0.057 | 0.835 | 2.84 × 10-3 |
| Binomial | Gaussian | Binomial | 100 | 0.504 | 0.091 | 0.617 | 3.63 × 10-3 | 0.098 | 0.762 | 2.03 × 10-3 | 0.059 | 0.834 | 2.75 × 10-3 |
| Poisson | Gamma | Gaussian | 100 | 0.588 | 0.162 | 0.023 | 1.28 × 10-4 | 0.502 | 0.776 | 1.28 × 10-4 | 0.176 | 0.798 | 0.017 |
| Poisson | Gamma | Poisson | 100 | 0.537 | 0.095 | 1.019 | 7.67 × 10-5 | 0.009 | 0.818 | 7.67 × 10-5 | 0.142 | 0.833 | 0.013 |
| Binomial | Gamma | Gaussian | 100 | 0.459 | 0.029 | 0.008 | 1.55 × 10-5 | 0.481 | 0.669 | 4.12 × 10-3 | 0.096 | 0.677 | 3.75 × 10-3 |
| Binomial | Gamma | Binomial | 100 | 0.549 | 0.113 | 0.517 | 1.15 × 10-4 | 0.021 | 0.634 | 6.87 × 10-3 | 0.131 | 0.650 | 5.59 × 10-3 |
| Poisson | Binomial | Gaussian | 100 | 0.673 | 0.126 | 0.534 | 0.039 | 0.371 | 0.599 | 0.025 | 0.265 | 1.133 | 0.014 |
| Poisson | Binomial | Poisson | 100 | 0.699 | 0.189 | 1847.624 | 1.70 × 1011 | 223.359 | 0.599 | 0.025 | 0.264 | 1.132 | 0.014 |
| Binomial | Binomial | Gaussian | 100 | 0.510 | 0.127 | 0.200 | 0.012 | 0.551 | 0.600 | 9.96 × 10-3 | 0.166 | 0.800 | 2.15 × 10-3 |
| Binomial | Binomial | Binomial | 100 | 0.491 | 0.094 | 0.717 | 0.011 | 0.146 | 0.600 | 0.010 | 0.167 | 0.800 | 2.16 × 10-3 |