## 4 Results
### Networks & Regression Models
We rank coefficient estimates in Table 9 by order of contribution (from positive estimates to negative estimates) and by coefficient size (magnitude). Here we are observant of the coefficient estimates and the direction and distribution of likely parameters generated by the permutations of the quadratic assignment procedure. That is, we are interested in rank order (of appearance), magnitude (absolute value), and the ensemble of networks with an exact structure to our observed network. Figure 7, Tables 8 and 9 summarize these quantities. The M1 regression model produces a straightforward linear system where more 'like' activity produces more matches. This is due to a positive intercept, positive like parameter estimate with a valid test statistic extant on the upper tail (\(Pr(b\)<=\(n\))), and greater differences in attractiveness. We find that only 55% of networks produced higher estimates than observed. Primarily, this is due to the systemic differences in how male and female agents evaluate age with males preferring slightly younger females and females preferring slightly older males. As a consequence, estimates are centered in a range that describe opposing positive and negative difference in age. By rank order of contribution, the like variable is the largest contributor to matches, followed by attractiveness, ethnicity, and then age. Ranked by magnitude, the like relation is the primary contributor to matches, while attractiveness and ethnicity contribute along the same rank, and age contrib \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Order of Contribution**} & \multicolumn{4}{c}{**Rank by Magnitude**} \\ \hline  & **M1** & **M2-F** & **M2-T** & **M1** & **M2-F** & **M2-T** \\ \hline \multirow{2}{*}{like network} & 1 & 4 & 5 & 1 & 1 & 1 \\  & & & 4 & & 1 \\  & & & 4 & & 1 \\  & & 2 & 3 & 2 & 2 & 2 \\  & 4 & 1 & 3 & 3 & 2 & 3 \\  & & 3 & 2 & 1 & 2 & 3 \\  & & X & X & X & X & X \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Parameter estimates ordered by contribution to match network (left compartment) from large values to smaller values (including negative values), and by magnitude rank (overall contribution), e.g., while the like relation for the M2-T model was a top contributor to the match dependent variable (rank by magnitude = 1), it was also a negative parameter estimate placing it 5 th in the order of contribution. roughly 5 times less than whether an agent likes another of an ideal difference in age versus 3 or more standard deviations away, placing it 3 rd in magnitude rank. It was a useful exercise in model validity to report two models for the M2 dating system--one which included the messaging network (M2-T) and one which omitted it (M2-F). The first clue in the non-applicability of M2-F's regression model is the relatively high residual standard error (0.25) when compared to the true model (0.076), an order of magnitude of difference. The non-inclusion of the messaging network as an independent variable caused the quadratic assignment procedure to shift the (positive) estimate for attractiveness and ethnicity to a negative estimate and assigned the parameter estimate for ethnicity a much smaller weighing (from \(10^{-6}\) to \(10^{-4}\)). Under conditions where this data may have been gathered from a real-world sample, one may be inclined to accept these differences at face-value, but because we know that a proper model must be inclusive of the messaging network--included in M2-T--since the behavior was incorporated in the simulation's specifications, we know that it must be false. The greater clue comes from the rankings of effects by magnitude (Table 9) which shows that M1 and M2-T have emerged the same order of effect ranking--that is, the variables contribute similar amount to the creation of a match for agents, while M2-F conveyed a differing order. Greater confidence in M2-T as a valid model begins with the standard error of the model, which was roughly equivalent to M1 (0.076, 0.097, respectively).