GIS-Integrated Agent-Based Model of Residential Solar PV Diffusion

however, the median home value of adopters has decreased from $391,00 to $371,000 from 2008 to 2012.Logistic regression was used to calculate the odds of a household adopting solar PV in Austin accordingto equation 6, where n is the number of households, Nei is the number of adopters within 1500ft, gis the home value decile, and HV C is a binary variable for each home value decile g. Empirically, wefind that the odds of adoption depend significantly on market value deciles , with higher odds for highermarket value deciles (results not shown here). This information is used to initialize the opinion thresholdfor agents depending on their wealth–thus, the opinion threshold of a household in the highest homevalue decile (> $510k) has an opinion threshold roughly 5 times higher than an equivalent household isthe 5 th home value decile ($166k-$193k). In future work, we will explore other model constructs thatemploy this empirical observation (odds of adoption depending on home value/wealth) more directly,for example by using it to initialize the payback thresholds.Adopt i =1 + e −(β0+ n ∑1∑( 10β gHV C g) i+β 2Nei i)i=1 g=1(6)2.7 Model EvaluationEach batch of the ABM was evaluated against empirical data in two ways: over time through deviation(RMSE) in marginal quarterly and cumulative quarterly adoption, and over space through spatial autocorrelationmapping of adopters. Models were said to perform better with lower RMSE, and a largernumber of matching spatial hot-spots.2.7.1 Root Mean Squared ErrorResiduals for the marginal number of new adopters and the cumulative number of adopters were calculatedby subtracting the model output for a given quarter from the empirical outcome in the samequarter. The deviation, or root mean squared error (RMSE) of the model was calculated accordingly,where q is a given quarter, â is the number of adopters in the model, and a is the number of adoptersin the empirical data:n∑RMSE = √ ( (â − a q) 2) (7)nq=1We assume that models with lower deviation more accurately represent the reality of aggregate consumerdecision-making processes.2.8 Hot-Spot AnalysisWe evaluated areas within the study area that empirically displayed clustering of PV adopters comparedto where these clusters were predicted by the ABM. To do this we divided the study area into 4000ftx 4000ft cells, and performed hot-spot analysis using the Getis-Ord G ∗ i test statistic to generate localestimates for significant spatial autocorrelation along 2000ft distance bands, where w ij is the spatialweight between cell i and cell j, x j is the number of adopters in that cell, ¯X is the mean number of8