The Professional Counselor | Volume 10, Issue 4 509 statistical results (Depaoli & van de Schoot, 2017). The WAMBS checklist consists of four stages and 10 points to appropriately understand, interpret, and provide results of Bayesian statistics. The following paragraph outlines these 10 steps as applied to the current data. First, normally distributed, non-informative priors were used (see Table 3). Second, model convergence was inspected by visually inspecting trace plots and using Geweke’s statistic. A visual inspection of the posterior parameter trace plots provided evidence of chain convergence in which each chain centers around a value and has few fluctuations displaying a “fuzzy” pattern. Geweke’s statistic compares the differences in means across chains to test convergence by comparing the first 10% of the chain to the last 50%. According to the Geweke’s statistics results, all values are within the range of +/- 1.96 and retain the null hypothesis with p > .05 (nonsignificant), indicating convergence. Convergence remained after doubling the number of iterations. Third, the chains did not appear to shift and converge at another location after doubling the iterations, with parameters centering around the previous estimates. Fourth, each parameter histogram was reviewed and determined to have adequate representation of the posterior distribution. Fifth, after determining the model had converged, the chains were inspected for dependency as evidenced by the autocorrelations. The model appeared to have low autocorrelations, with each chain approaching and reaching zero between 10 and 20 lags, indicating low chain dependency. In addition to low autocorrelations, the effective sample size indicated the model was robust with information as evidenced by (ESS > 10,000) and positive efficiency. Prior to interpreting the output, we compared the model using the informative prior information, which slightly pulled the posterior mean estimates closer to that of the prior information; however, the results were effectively the same. Sixth, the posterior distribution appeared to make substantive sense as evidenced by smooth posterior density plots with reasonable standard deviations within the scale of the original parameters. Steps 7 through 9 were skipped in cases where only non-informative priors were used. Lastly, Step 10, the Bayesian way of interpreting and reporting results, was followed. To answer the first research question, the post-summary means that are group deviations from the grand mean (intercept) were taken to determine the differences of Carnegie classification in comparison to R1, yielding the parameter estimate B (see Table 3). Table 3 Posterior Summaries Parameter Priors M HPD Interval B exp(B) 1/exp(B) Intercept N (0, 10) 1.612 1.4251 1.8018 3.521 - - R1 N (0, 10) 1.909 1.6013 2.2142 - - - R2 N (-0.27, 10) 1.628 1.3315 1.9199 -0.28 0.756 1.323 D/PU N (-.66, 10) 0.612 0.3142 0.9038 -1.295 0.274 3.650 M1 N (-1.17, 10) 0.317 0.0617 0.5824 -1.587 0.206 4.854 M2 N (-1.17, 10) -0.712 -1.0935 -0.3411 -2.619 0.073 13.699 M3 N (-1.17, 10) -1.164 -1.8311 -0.4917 -3.082 0.046 21.740 Bacc N (2, 10) -1.609 -2.4932 -0.7119 -3.512 0.029 34.483 SF N (2, 10) -0.982 -1.5083 -0.4479 -2.897 0.055 18.182 Dispersion N (1, 1) 0.885 0.7506 1.0275 1.118 - - Note: exp(B) reflects the times fewer publications in relation to R1; 1/exp(B) reflects R1 x more publications in relation to parameter.
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