## 3 Model Comparison  
As we have noted, our objective is to compare two models with varied multiplicity levels in terms of aggregate outcomes. We chose to focus our effort on matches that agents accumulate in each model. We carried out a formal inquiry of the statistical parameters and distributions of likes, messages, and matches as well as evaluated conditional distributionsthrough a network regression--the Multiple Regression Quadratic Assignment Procedure--a suitable method for our analysis that accounts for our model's rule dependencies without inappropriate assumptions. While the literature on methods of network comparisons is copious [84], we chose MRQAP for its minimal assumptions, ability to include heterogeneous agent profiles, and for its relative ease of interpretation, reducing output comparisons to a comparison of coefficients of a regression model. The Multiple Regression Quadratic Assignment Procedure (MRQAP) is used to test for significance in an observed correlation where dependency between two or more dyadic relations may exist [17]. MRQAP relies on a non-parametric permutation-based test that preserves the integrity of the observed network structure to report confidence. This approach was originally developed by [PERSON] and colleagues [15] to identify geographic clustering of diseases [17]. [PERSON] et al. noted that covariates in geographic datasets are highly co-dependent and typically not independently and identically distributed (_i.i.d._) due to a co-evolution of relational processes. Consequently, the covariates are unsuitable for regression models that assume independence of observations--such as the method of Ordinary Least Squares (OLS). MRQAP has been developed and deployed as a mainstream network analysis tool. The procedure is particularly useful when calculating coefficient magnitudes and parameter estimates, and as a corollary, the strength of social effects through permutations of network statistics. Since our synthetic population samples, rules, attributes, and mechanisms are not _i.i.d._, we relied on this standard social network analysis model to compare outputs from our simulations. To summarize the method's mechanics: MRQAP provides regression coefficients as does classical regression models (ordinary least squares), but its' assumptions do not fall within the General Linear Model (GLM). Since we cannot guarantee some of the basic assumptions of OLS when considering relational data structures--assumptions such as bivariate normality or the independence of observations--MRQAP calculates coefficient estimates as does a linear regression procedure, but permutes the dependent and independent variables on the structure of the network [85] yielding conditional \(p\)-values. Simply put, MRQAP answers: How likely is a model description given a randomization of the dependent variable on the network's structure? As we have explained, MRQAP is well-suited for our comparative aims: Consider that M1 (Figure 3) emulates the simplest dating application interface--an example we repeatedly cite is Tinder. We begin our analysis by considering likes and matches as edges in a network (ties), and thus we frame our output analysis as a network analysis with edges within both simulations' code-base reflecting all temporal interactions through the application's interface as edges in a network. Our analysis is then conducted using the cross-sectional network emerged from the temporal interactions. Framing our analysis in this way allows for the use of MRQAP and its powerful permutation-based statistical assumptions while accounting for non-independence in our model with minimal interfering assumptions. To compare M1 to M2, we consider their shared output; In this case the common output is matches. We ensure that inputs among the two models are identical for a one-to-one comparison. A synthetic population instantiated for M1 can apply M2's behavioral rules without loss of generality and vice versa.