Fig 1.
An example of induced iterations in GLM with main effects only.
The linear predictor (left panel) shows constant difference between the three lines. On the natural scale (right panel), we see varying distance between the three lines, which is an interaction induced by the back-transformation of the logit model. Here, the solid line is β = 1; the dashed line is β = 2; and the dotted line is β = 3.
Table 1.
Coding scheme for response and explanatory variables used in GLM analysis of cyber abuse.
Table 2.
Descriptive statistics for response and explanatory variables in GLM analysis of cyber abuse.
Table 3.
Proportion of cases of indirect cyber abuse for various combinations of variables.
Table 4.
Summary of generalized linear model of indirect cyber abuse using a single factor with four levels (Eq 11).
Table 5.
Summary of coefficient estimates for full GLM model (Eq 12).
Table 6.
Summary of model testing using the change in deviance.
Significant outcomes indicate that the dropping of a term results in a significantly worse fit.
Table 7.
Summary of coefficient estimates for the main effects GLM.
This model was determined using change in deviance (see Table 6).
Fig 2.
Change in deviance test applied to pedagogical example.
The gradated grey line represents the back- transformation of the logit function (inverse logit). The grey levels in this line indicate the gradient of the function, with darker areas having the steepest slopes. The gradient is also represented by the black dashed line and the right axis. The coloured points indicate various subgroups and the size of these points represents their sample size. Solid coloured lines represent the linear predictors obtained from the full model including an interaction term. The coloured dashed lines represent linear predictors from the main effects model.
Table 8.
Results of determining model using change in deviance.
Fig 3.
Three vague Normal priors used to compute Bayesian logistic regression.
Top: Prior distribution used for the intercept parameter β0 (Eq 12), which represents persons with no prior relationship and instrumental motivation (N(−1, 2)). Middle: Prior distribution used for parameters β1,2, which represents the additional effect of persons with either a prior relationship OR an expressive motivation over the intercept value (N(0.1, 0.5)). Bottom: Prior distribution chosen to represent β3, the additional effect of both having a prior relationship and expressive motivation (N(1.1, 2)). Grey areas represent regions allowed in the prior that are the opposite of our hypothesis.
Table 9.
Summary statistics of Bayesian GLM using vaguely informative priors.
Fig 4.
Posterior distributions of coefficients (left column), linear predictors (middle column) and predictive fits (right column).
Table 10.
Summary statistics from the Bayesian Model Averaging analysis*.
Fig 5.
A graph of the selected models explaining the use of indirect methods of abuse using Bayesian Model Averaging analysis.
Width of individual rectangles reflects the posterior probability of each model being correct.
Table 11.
Comparison of coefficients and standard errors from standard GLM, Bayesian GLM posterior estimates (using vague priors) and GLM posterior estimates via BMA.
Table 12.
Proportions used for simulations of population in each Rel-Mot†subgroup and method of abuse.
Table 13.
Models chosen using change in deviance criteria.
Fig 6.
Estimated posterior mean for coefficients using BMA (black) with 20%, 50% and 95% credible intervals.
Grey represents distribution of parameters from standard GLM with 95% range of estimates.
Table 14.
Inclusion probabilities of coefficients of interest from the simulation study.
Each sample size consisted of 1000 simulations. Cell sample size (n) differs between simulations based on the probabilities in Table 12.
Fig 7.
Distribution of estimated inclusion probabilities for each coefficient using data from the simulation study.
Fig 8.
Density of predictions based on models using change in deviance (left) and BMA (right).
Solid black line represents results N = 1000, medium grey dashed line N = 500, and light grey dotted line is N = 110. True population proportion indicated by grey vertical line.
Table 15.
Comparison of statistical techniques and their main benefits.