## 4 Results
### Networks & Regression Models
\begin{table}
\begin{tabular}{l c c c} \hline  & **M1** & **M2 (False)** & **M2 (True)** \\ \hline like network & \(2.55\times 10^{-1}\) & \(-6.05\times 10^{-3}\) & \(-6.06\times 10^{-3}\) \\ \(Pr(<=b)\) & (1.0) & (0.0) & (0.0) \\ \(Pr(>=b)\) & (0.0) & (1.0) & (1.0) \\ \(Pr(>=|b|)) & (0.0) & (0.0) & (0.0) \\ \hline message network & & & \(-4.35\times 10^{-3}\) \\ \(Pr(<=b)\) & & & (0.0) \\ \(Pr(>=b)\) & & & (1.0) \\ \(Pr(>=|b|)\) & & & (0.0) \\ \hline attractiveness (difference) & \(2.04\times 10^{-4}\) & \(-6.87\times 10^{-4}\) & \(1.64\times 10^{-4}\) \\ \(Pr(<=b)\) & (0.8) & (0.93) & (0.92) \\ \(Pr(>=b)\) & (0.2) & (0.07) & (0.01) \\ \(Pr(>=|b|)\) & (0.45) & (0.14) & (0.1) \\ \hline age (difference) & \(2.02\times 10^{-7}\) & \(1.64\times 10^{-4}\) & \(-4.96\times 10^{-6}\) \\ \(Pr(<=b)\) & (0.55) & (0.01) & (0.01) \\ \(Pr(>=b)\) & (0.45) & (0.99) & (0.99) \\ \(Pr(>=|b|)\) & (0.99) & (0.03) & (0.03) \\ \hline ethnicity (difference) & \(1.24\times 10^{-4}\) & \(-4.00\times 10^{-6}\) & \(2.14\times 10^{-4}\) \\ \(Pr(<=b)\) & (0.70) & (0.78) & (0.8) \\ \(Pr(>=b)\) & (0.30) & (0.22) & (0.2) \\ \(Pr(>=|b|)\) & (0.65) & (0.38) & (0.42) \\ \hline intercept & \(3.15\times 10^{-3}\) & \(5.88\times 10^{-3}\) & \(5.90\times 10^{-3}\) \\ \(Pr(<=b)\) & (1.0) & (1.0) & (1.0) \\ \(Pr(>=b)\) & (0.0) & (0.0) & (0.0) \\ \(Pr(=|b|)\) & (0.0) & (0.0) & (0.0) \\ \hline Permutation(s) & 100 & 100 & 100 \\ R\({}^{2}\) & 0.1809 & 0.000205 & 0.000218 \\ Adjusted R\({}^{2}\) & 0.1809 & 0.00020 & 0.00021 \\ Residual Std. Error (df = 998,995) & 0.097 & 0.25 & 0.076 \\ F Statistic (df = 4; 998,995) & 55,170 & 51.24 & 43.59 \\ \hline \end{tabular} Note: models are statistically significant at the \(p<0.0001\) level.  
\end{table} 
Table 8: Multiple regression model of monadic and dyadic covariates using the quadratic assignment procedure. One model for Tinder-type applications (M1) and two models for Hinge-like applications (M2) are shown. The Message relation covariate is only included in the second model of the M2 model for comparison. Reported are the parameter estimates and \(p\)-value estimates for each effect. \(Pr(<=)\) conveys the proportion [0, 1] of networks generated/permuted with identical structure to the observed network with a parameter value less than or equal to the reported estimate. \(Pr(>=)\) conveys the reverse with the proportion of permuted networks with a parameter value greater than observed. \(Pr(>|=|)\) reveals symmetrical properties of the parameter distribution with nil indicating perfect symmetry and other values indicating skewness. resulted in parameters for the like relation that were smaller (<=\(b\))) than the observed effect size of 0.255 and that were larger than (>=\(b\))) \(-\)0.0061 for M2-F and \(-\)0.0061 for M2-T. This represents high confidence that this parameter differs significantly from a random observation of the same structural network. Further reported is a two-tailed measure of confidence (\(Pr(>|=|)\)) expressing the skewness of the sampling distribution of estimates. The three models presented in Table 8 explore a true model for M1 with all available monadic and dyadic effects, a false model for M2 (M2-F) without the messaging network, and a second model for M2 with messaging included. It was clear that all models are significant when compared to random. M2-F generated a model with a much higher standard error (0.25) when compared with M1 (0.097) and the true M2-T model (0.076). The coefficient of determination for the M1 model (\(R^{2}=0.18\)) was greater than both M2 model equivalents, given that the number of agent decision points needed to achieve a match are more numerous in the M2 model regressions. Each of these decision points are subject to additional (uniform) random draws. This increases the amount of uniform random noise in simulation runs but leaves the reliability of the models intact. Beyond model-level reliability and validity, our virtual experiment provides agreeable results.