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The slope of the stochastic versus dispersion NO2 regression equation is only slightly > 1, whereas the slope of the PM2.5 versus TSP regression equation is > 3. Note that, although the correlation between measured NO2 and PM2.5 concentrations was 0.84, the correlation between modeled NO2 and PM concentrations was almost 1 for both models (data not shown).
Yang, 2013 Chinese A-share listed companies Top management team Tournament theory; justice theory Pay dispersion Linear regression Pay dispersion among top management teams was positively related to turnover rates.
The magnitude of the average biases across the 20,000 replicate experiments is similar across these three models when the data are beta distributed (Table 4); however, when the data arise from a multinomial distribution the variable-dispersion beta regression model has slightly elevated bias levels compared to the linear regression model and fractional logit regression model.
The variable-dispersion beta regression model assumes that the mean and dispersion of these random variables can be represented in the following form: g μ i = η i = β 0 + β 1 X i 1 h ϕ i = ζ i = γ 0 + γ 1 X i 1 Once again, we assume that both g and h are strictly monotonic, twice differentiable functions which act to map the mean, μi, and the dispersion, ϕ i, to the real line.
The variable-dispersion beta regression model is unbiased (given proper specification of the dispersion sub-model).
As its name implies, the variable-dispersion beta regression model [ 5] allows the value of the dispersion parameter to vary across individuals.
Further when response data are distributed according to a discrete multinomial distribution minor advantages in power appear for the variable-dispersion beta regression model (at the cost of small magnitude increases in bias) and the fractional logit model compared to the linear regression model (Table 6).
In the power experiments, variable-dispersion beta regression and fractional logit regression models have slightly elevated power compared to linear regression models.
The variable-dispersion beta regression model and fractional logit model appear slightly more powerful than the linear regression model when a non-zero difference between groups is present.
Again the variable-dispersion beta regression model and the fractional logit regression model have elevated type-1 error rates when sample sizes are small (N0 = N1 = 25).
Moreover, the power and type-1 error profiles are very similar for the linear model, variable-dispersion beta regression model and the fractional logit regression model.
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