PV adoption
This code is just for visualizing the findings rather than running model.
Load packages
Load Data
load("dat_all3.RData")Visualize vermont causal flows
gn_vm
- The center and northeast parts have low density of causal links due to the mountainous geography.
- Dense causal links with bi-directionality exist in the northwest region where urbanized areas are located.
- Neighborhood diffusion–within tract diffusion of PV adoption–occurs strongly in Burlington area (the most populated northwestern region), identified by high mutual information. Other areas with high mutual information tend to be those with high population density.
Visualize Seattle causal flows
gn_sea
- Rivers hinder PV adoption diffusion across tracts are contiguous.
- It is less likely to mutual causal links.
Transfer Entropy comparison
ted## Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(density)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
- Transfer entropy in average is greater in Vermont, yet transfer entropy per distance is greater in Seattle.
Indegree, Outdegree, Netdegree, and Betweenness in Vermont
plot_net_prop2(df_vm,te_vm,pval_vm,neighbor_vm,VT_acs_2019)
- Probably link these figures in explaining maps of causal flows?
- Depending on the situation, this may go to supplementary materials
- Netdegree = Indegree - Outdegree
- Betweenness centrality: a tract being a transit in causal connections
Indegree, Outdegree, Netdegree, and Betweenness in Seattle
plot_net_prop2(df_sea,te_sea,pval_sea,neighbor_sea,seattle_tracts2)
NEIGHBORHOOD SPILLOVER - Within tract spillover
Used mutual information:
\(MI[X_t;X_{t+1}] = \sum q(x_t, x_{t_1}) \cdot log \left(\frac{q(x_t, x_{t_1})}{q(x_t) q(x_{t_1})} \right)\)
Logistic regression for mutual information in Vermont
stargazer::stargazer(
m0_vm,m4_vm,m5_vm,m6_vm,m1_vm,m2_vm,m3_vm,
type = "text", digits = 2
)##
## ==================================================================================
## Dependent variable:
## ----------------------------------------------------------------
## Mutinfo
## (1) (2) (3) (4) (5) (6) (7)
## ----------------------------------------------------------------------------------
## logpop 2.19*** 1.92*** 1.56***
## (0.35) (0.36) (0.38)
##
## SingleFamily -3.54* -2.55 -2.83 -2.43 -2.00 -2.15
## (2.10) (2.21) (2.34) (2.62) (2.65) (2.67)
##
## Edu 1.94 2.01 1.54 4.06** 3.73* 2.97
## (1.58) (1.73) (1.89) (1.93) (1.98) (2.04)
##
## HomeOwn -8.42*** -6.34*** -5.06** 1.68 1.81 1.46
## (1.97) (2.07) (2.18) (2.76) (2.79) (2.87)
##
## Income 0.0001*** 0.0000* 0.0000 0.0000* 0.0000 0.0000
## (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000)
##
## White 5.34 4.52 4.82 8.15 7.68 7.26
## (5.11) (5.69) (6.51) (6.60) (6.92) (7.46)
##
## Ininfo 12.55*** 6.66**
## (2.72) (2.84)
##
## Totinfo 12.08*** 7.92***
## (2.07) (2.13)
##
## Constant -0.23* -1.26 -1.20 -2.23 -27.42*** -24.58*** -21.00**
## (0.13) (4.88) (5.44) (6.19) (7.40) (7.77) (8.32)
##
## ----------------------------------------------------------------------------------
## Observations 248 246 246 246 246 246 246
## Log Likelihood -170.32 -134.56 -118.78 -102.48 -101.76 -98.48 -91.86
## Akaike Inf. Crit. 342.63 281.12 251.56 218.96 217.52 212.96 199.72
## ==================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Dependent variable: Mutual information is significant or not (binary), in other words, neighborhood PV adoption diffusion exists or not.
Indep. variable:
logpop - logged population (not density but in numbers)
RiskRate - National Risk Index -> high value means that the tract is at risk
for 18 natural hazards
Ininfoc - the number of incoming causal flows
Totinfoc - the number of both incoming and outgoing causal flows- More populous tracts are likely to have more neighborhood diffusion.
- Adding population variable increases AIC but looses significance of other independent variables perhaps because of its strong effect.
- Highly-educated and high-income tracts are likely to have internal diffusion of rooftop PV adoption.
- Lower Home-own variable leads to greater neighborhood diffusion of PV adoption. ## Not clear why for now
- Greater risk rate significantly affects more neighborhood diffsion. ## Not sure why
- Tract-tract diffusion (transfer entropy; Ininfoc & Totinfoc) tends to reinforce neighborhood diffusion. ## Not clear which one to use between Ininfoc vs Totinfoc.
Logistic regression for mutual information in Seattle
stargazer::stargazer(
m0_sea,m4_sea,m5_sea,m6_sea,m1_sea,m2_sea,m3_sea,
type = "text", digits = 2
)##
## ===================================================================================
## Dependent variable:
## -----------------------------------------------------------------
## Mutinfo
## (1) (2) (3) (4) (5) (6) (7)
## -----------------------------------------------------------------------------------
## logpop 2.70*** 2.52*** 2.16***
## (0.78) (0.79) (0.83)
##
## SingleFamily 4.22 3.93 3.85 5.51* 4.98 4.27
## (2.83) (2.96) (3.47) (3.21) (3.29) (3.71)
##
## Edu -3.70 -4.94 -7.26** -3.20 -3.98 -6.25
## (3.05) (3.20) (3.59) (3.37) (3.46) (3.80)
##
## HomeOwn -0.16 -0.25 -0.81 1.75 1.84 1.28
## (3.02) (3.04) (3.39) (3.34) (3.36) (3.63)
##
## Income 3.31** 3.58** 4.12** 2.71 2.75 3.25
## (1.66) (1.74) (1.99) (1.79) (1.83) (2.06)
##
## White -0.21 0.65 1.99 -0.04 0.71 2.09
## (2.00) (2.09) (2.26) (2.23) (2.34) (2.51)
##
## Ininfo 10.97** 7.24
## (5.51) (5.68)
##
## Totinfo 16.87*** 14.61***
## (4.46) (4.54)
##
## Constant -0.63*** -4.03*** -4.33*** -4.91*** -41.29*** -38.95*** -34.38***
## (0.18) (1.17) (1.22) (1.36) (11.05) (11.11) (11.60)
##
## -----------------------------------------------------------------------------------
## Observations 132 132 132 132 132 132 132
## Log Likelihood -85.34 -63.89 -61.84 -53.78 -56.58 -55.74 -49.88
## Akaike Inf. Crit. 172.68 139.77 137.67 121.56 127.15 127.49 115.76
## ===================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Dependent variable: Mutual information is significant or not (binary), in other words, neighborhood PV adoption diffusion exists or not.
Indep. variable:
logpop - logged population (not density but in numbers)
RiskRate - National Risk Index -> high value means that the tract is at risk
for 18 natural hazards
Ininfoc - the number of incoming causal flows
Totinfoc - the number of both incoming and outgoing causal flows- More populous tracts are likely to have more neighborhood diffusion.
- Adding population variable increases AIC but looses significance of other independent variables perhaps because of its strong effect.
- Housing-related variable (SingleFamily) is more important in neighborhood diffusion of Seattle than that of Vermont.
- Higher income tends to lead to active neighborhood diffusion as in the Vermont case. However, education is not significant anymore.
- Greater risk rate significantly affects more neighborhood diffsion. ## Not sure why
- Tract-tract diffusion (transfer entropy; Ininfoc & Totinfoc) is less likely to reinforce neighborhood diffusion in Seattle. ## Not clear which one to use between Ininfoc vs Totinfoc.
TRACT-TRACT SPILLOVER
Transfer entropy is calculated to capture tract-tract diffusion
\(TE[X;Y] = \sum q(x_t, x_{t_1}, y_t) \cdot log \left(\frac{q(x_{t+1} |x_t, y_t)}{q(x_{t+1}|x_t)} \right)\)
Exponential Random Graph Model for receiving tract-tract diffusion in Vermont
summary(in_vm2)## Call:
## ergm(formula = net_vm ~ edges + nodeicov("HomeOwn") + nodeicov("SingleFamily") +
## nodeicov("Edu") + nodeicov("White") + nodeicov("Income") +
## nodeifactor("RiskRate") + nodeifactor("Mutinfo"))
##
## Maximum Likelihood Results:
##
## Estimate Std. Error MCMC % z value Pr(>|z|)
## edges -6.838e+00 1.475e+00 0 -4.637 <1e-04 ***
## nodeicov.HomeOwn -8.930e-01 6.218e-01 0 -1.436 0.1509
## nodeicov.SingleFamily -1.065e+00 6.847e-01 0 -1.555 0.1199
## nodeicov.Edu -4.162e-01 4.990e-01 0 -0.834 0.4043
## nodeicov.White 1.648e+00 1.602e+00 0 1.028 0.3039
## nodeicov.Income 2.718e-05 4.704e-06 0 5.778 <1e-04 ***
## nodeifactor.RiskRate.3 -1.675e-01 1.244e-01 0 -1.347 0.1780
## nodeifactor.RiskRate.4 -3.227e-01 1.700e-01 0 -1.898 0.0577 .
## nodeifactor.RiskRate.5 -1.637e-01 3.088e-01 0 -0.530 0.5960
## nodeifactor.Mutinfo.1 6.616e-01 1.141e-01 0 5.801 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 83552 on 60270 degrees of freedom
## Residual Deviance: 5158 on 60260 degrees of freedom
##
## AIC: 5178 BIC: 5268 (Smaller is better. MC Std. Err. = 0)Dependent variable: Transfer entropy is significant or not (binary), in other words, tract-tract PV adoption causal flow exists or not (with directionality).
Indep. variable:
* "nodeicov" means that the attribute is for tracts of incoming causal
flows, e.g., nodeicov.Income = income values at the tracts where causal
flows set as destinations (recepter of PV adoption diffusion)
** "nodeifactor" is for categorical variables
*** From now on, given that causal flow "tract A -> tract B", I will call
tract A as a diffuser and tract B as a recepter. Happy to change terms
later on.
RiskRate - National Risk Index -> high value means that the tract is at risk
for 18 natural hazards
1 - Very low
2 - Relatively low
3 - Relatively moderate
4 - Relatively high
5 - Very high
Mutinfo.1 - Existence of mutual information (neighborhood diffusion) in the
sending/receiving tracts.- Census attributes are not significant for recepters–weak pull forces of tract-tract PV adoption diffusion–except for income. High-income tracts are likely to adopt rooftop PV from diffusers.
- Tracts with high mutual information tends to adopt rooftop PV from neighbor tracts. That is, neighborhood diffusion reinforces tract-tract diffusion in Vermont.
- Environmental risks do not matter in accepting tract-tract diffusion from the receiver’s perspective.
Exponential Random Graph Model for sending tract-tract diffusion in Vermont
summary(out_vm2)## Call:
## ergm(formula = net_vm ~ edges + nodeocov("HomeOwn") + nodeocov("SingleFamily") +
## nodeocov("Edu") + nodeocov("White") + nodeocov("Income") +
## nodeofactor("RiskRate") + nodeofactor("Mutinfo"))
##
## Maximum Likelihood Results:
##
## Estimate Std. Error MCMC % z value Pr(>|z|)
## edges -4.676e+00 1.370e+00 0 -3.414 0.000640 ***
## nodeocov.HomeOwn -9.030e-01 6.180e-01 0 -1.461 0.143976
## nodeocov.SingleFamily -3.049e-01 6.977e-01 0 -0.437 0.662085
## nodeocov.Edu -2.404e-01 4.938e-01 0 -0.487 0.626352
## nodeocov.White -1.057e+00 1.522e+00 0 -0.694 0.487386
## nodeocov.Income 1.801e-05 4.682e-06 0 3.847 0.000119 ***
## nodeofactor.RiskRate.3 -9.060e-02 1.287e-01 0 -0.704 0.481558
## nodeofactor.RiskRate.4 -1.793e-01 1.685e-01 0 -1.064 0.287440
## nodeofactor.RiskRate.5 -6.776e-01 3.944e-01 0 -1.718 0.085790 .
## nodeofactor.Mutinfo.1 1.202e+00 1.239e-01 0 9.698 < 1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 83552 on 60270 degrees of freedom
## Residual Deviance: 5075 on 60260 degrees of freedom
##
## AIC: 5095 BIC: 5185 (Smaller is better. MC Std. Err. = 0)Dependent variable: Transfer entropy is significant or not (binary), in other words, tract-tract PV adoption causal flow exists or not (with directionality).
Indep. variable:
* "nodeocov" means that the attribute is for tracts of outgoing causal
flows, e.g., nodeocov.Income = income values at the tracts where causal
flows set as origin/source (diffuser of PV adoption diffusion)
** "nodeofactor" is for categorical variables
*** From now on, given that causal flow "tract A -> tract B", I will call
tract A as a diffuser and tract B as a recepter. Happy to change terms
later on.
RiskRate - National Risk Index -> high value means that the tract is at risk
for 18 natural hazards
1 - Very low
2 - Relatively low
3 - Relatively moderate
4 - Relatively high
5 - Very high
Mutinfo.1 - Existence of mutual information (neighborhood diffusion) in the
sending/receiving tracts.- Lower homeown values lead to more mobilized tract-tract diffusion. High-income tracts are likely to adopt rooftop PV from diffusers.
- Tracts with high mutual information tends to adopt rooftop PV from neighbor tracts. That is, neighborhood diffusion reinforces tract-tract diffusion in Vermont.
- Summing up the results from previous Vermont models, neighborhood diffusion and tract-tract diffusion are coupled in PV adoption.
- Environmental risks do not matter in sending tract-tract diffusion from the receiver’s perspective.
Exponential Random Graph Model for receiving tract-tract diffusion in Seattle
summary(in_sea2)## Call:
## ergm(formula = net_sea ~ edges + nodeicov("HomeOwn") + nodeicov("SingleFamily") +
## nodeicov("Edu") + nodeicov("White") + nodeicov("Income") +
## nodeifactor("RiskRate") + nodeifactor("Mutinfo"))
##
## Maximum Likelihood Results:
##
## Estimate Std. Error MCMC % z value Pr(>|z|)
## edges -6.3920 0.6462 0 -9.892 < 1e-04 ***
## nodeicov.HomeOwn -0.5493 1.2229 0 -0.449 0.65332
## nodeicov.SingleFamily 3.0592 1.0614 0 2.882 0.00395 **
## nodeicov.Edu 1.7477 1.2309 0 1.420 0.15564
## nodeicov.White -1.9276 0.8124 0 -2.373 0.01765 *
## nodeicov.Income -0.3224 0.5806 0 -0.555 0.57869
## nodeifactor.RiskRate.3 0.5355 0.2473 0 2.165 0.03036 *
## nodeifactor.RiskRate.4 0.2834 0.3803 0 0.745 0.45621
## nodeifactor.RiskRate.5 -0.2330 1.0632 0 -0.219 0.82652
## nodeifactor.Mutinfo.1 0.2627 0.2005 0 1.310 0.19010
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 23972 on 17292 degrees of freedom
## Residual Deviance: 1552 on 17282 degrees of freedom
##
## AIC: 1572 BIC: 1650 (Smaller is better. MC Std. Err. = 0)Dependent variable: Transfer entropy is significant or not (binary), in other words, tract-tract PV adoption causal flow exists or not (with directionality).
Indep. variable:
* "nodeicov" means that the attribute is for tracts of incoming causal
flows, e.g., nodeicov.Income = income values at the tracts where causal
flows set as destinations (recepter of PV adoption diffusion)
** "nodeifactor" is for categorical variables
*** From now on, given that causal flow "tract A -> tract B", I will call
tract A as a diffuser and tract B as a recepter. Happy to change terms
later on.
RiskRate - National Risk Index -> high value means that the tract is at risk
for 18 natural hazards
1 - Very low
2 - Relatively low
3 - Relatively moderate
4 - Relatively high
5 - Very high
Mutinfo.1 - Existence of mutual information (neighborhood diffusion) in the
sending/receiving tracts.- Tracts with higher “SingleFamily” tend to be causally affected by neighboring tracts in Seattle (being receivers).
- Tracts with lower “White” tend to be causally affected by neighboring tracts in Seattle.
- Tracts with comparatively lower environmental risk adopt rooftop PV more. Note that general environmental risk ratings are
- Neighborhood diffusion does not matter tract-tract diffusion (decoupled).
Exponential Random Graph Model for sending tract-tract diffusion in Seattle
summary(out_sea2)## Call:
## ergm(formula = net_sea ~ edges + nodeocov("HomeOwn") + nodeocov("SingleFamily") +
## nodeocov("Edu") + nodeocov("White") + nodeocov("Income") +
## nodeofactor("RiskRate") + nodeofactor("Mutinfo"))
##
## Maximum Likelihood Results:
##
## Estimate Std. Error MCMC % z value Pr(>|z|)
## edges -5.95612 0.65711 0 -9.064 <1e-04 ***
## nodeocov.HomeOwn 0.16776 1.22408 0 0.137 0.8910
## nodeocov.SingleFamily 1.48957 1.08566 0 1.372 0.1701
## nodeocov.Edu 1.84880 1.28854 0 1.435 0.1513
## nodeocov.White -1.69725 0.82527 0 -2.057 0.0397 *
## nodeocov.Income -0.34259 0.57373 0 -0.597 0.5504
## nodeofactor.RiskRate.3 -0.02336 0.22452 0 -0.104 0.9171
## nodeofactor.RiskRate.4 -0.17029 0.35360 0 -0.482 0.6301
## nodeofactor.RiskRate.5 -0.60766 1.06175 0 -0.572 0.5671
## nodeofactor.Mutinfo.1 0.97835 0.21017 0 4.655 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 23972 on 17292 degrees of freedom
## Residual Deviance: 1532 on 17282 degrees of freedom
##
## AIC: 1552 BIC: 1630 (Smaller is better. MC Std. Err. = 0)Dependent variable: Transfer entropy is significant or not (binary), in other words, tract-tract PV adoption causal flow exists or not (with directionality).
Indep. variable:
* "nodeocov" means that the attribute is for tracts of outgoing causal
flows, e.g., nodeocov.Income = income values at the tracts where causal
flows set as origin/source (diffuser of PV adoption diffusion)
** "nodeofactor" is for categorical variables
*** From now on, given that causal flow "tract A -> tract B", I will call
tract A as a diffuser and tract B as a recepter. Happy to change terms
later on.
RiskRate - National Risk Index -> high value means that the tract is at risk
for 18 natural hazards
1 - Very low
2 - Relatively low
3 - Relatively moderate
4 - Relatively high
5 - Very high
Mutinfo.1 - Existence of mutual information (neighborhood diffusion) in the
sending/receiving tracts.- Census attributes are not significant for senders except for white. Low-white tracts are more likely to diffuse rooftop PV to neighboring tracts.
- Tracts with high mutual information tends to diffuse rooftop PV to neighbor tracts. That is, neighborhood diffusion reinforces sending effects of tract-tract diffusion in Seattle. Yet, the neighborhood and tract-tract diffusion is partially coupled in overall.
Exponential Random Graph Model for homophily in Vermont
summary(homo_vm)## Call:
## ergm(formula = net_vm ~ edges + mutual + gwesp(decay = 0.01,
## fixed = TRUE, type = "OTP") + absdiff("HomeOwn") + absdiff("SingleFamily") +
## absdiff("Edu") + absdiff("White") + absdiff("Income"))
##
## Monte Carlo Maximum Likelihood Results:
##
## Estimate Std. Error MCMC % z value Pr(>|z|)
## edges -5.537e+00 1.048e-01 0 -52.848 <1e-04 ***
## mutual 4.510e+00 2.066e-01 0 21.830 <1e-04 ***
## gwesp.OTP.fixed.0.01 1.582e+00 8.754e-02 0 18.069 <1e-04 ***
## absdiff.HomeOwn 3.966e-01 3.743e-01 0 1.060 0.2893
## absdiff.SingleFamily -3.046e-01 4.344e-01 0 -0.701 0.4832
## absdiff.Edu -1.709e+00 3.948e-01 0 -4.328 <1e-04 ***
## absdiff.White -1.678e+00 1.069e+00 0 -1.570 0.1165
## absdiff.Income -8.174e-06 3.505e-06 0 -2.332 0.0197 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 83552 on 60270 degrees of freedom
## Residual Deviance: 3790 on 60262 degrees of freedom
##
## AIC: 3806 BIC: 3878 (Smaller is better. MC Std. Err. = 1.747)Dependent variable: Transfer entropy is significant or not (binary), in other words, tract-tract PV adoption causal flow exists or not (with directionality).
Indep. variable:
* "mutual" means that a causal flow has reciprocity (A <-> B)
** "gwesp.OTP.fixed.0.01" is that if there is A -> B causal flow, it is
likely to have multiple transitting tracts indirectly shaping A -> B,
e.g., A -> C -> B & A -> D -> B if A -> B exists.
*** "absdiff" calculates absolute difference of an attribute in the causally
affecting and affected tracts in the homophily context. If the coeff. is
negative, tracts with similar attribute values tend to be causally
linked.
- Bi-directional causal flows are observed more than expected in Vermont.
- Causal flows tend to share transits for indirect causal links.
- Housing variables (SingleFamily, HomeOwn) are not significant in creating causal connections in Vermont.
- Causal flows emerge in two tracts with similar education levels and incomes.
Exponential Random Graph Model for homophily in Seattle
summary(homo_sea)## Call:
## ergm(formula = net_sea ~ edges + mutual + gwesp(decay = 0.01,
## fixed = TRUE, type = "OTP") + absdiff("HomeOwn") + absdiff("SingleFamily") +
## absdiff("Edu") + absdiff("White") + absdiff("Income"))
##
## Monte Carlo Maximum Likelihood Results:
##
## Estimate Std. Error MCMC % z value Pr(>|z|)
## edges -3.4007 0.1899 0 -17.907 < 1e-04 ***
## mutual 2.7113 0.3591 0 7.550 < 1e-04 ***
## gwesp.OTP.fixed.0.01 0.9709 0.1619 0 5.996 < 1e-04 ***
## absdiff.HomeOwn -1.6744 0.7935 0 -2.110 0.03484 *
## absdiff.SingleFamily -2.0675 0.7632 0 -2.709 0.00675 **
## absdiff.Edu -7.0657 1.2122 0 -5.829 < 1e-04 ***
## absdiff.White -2.6549 0.9536 0 -2.784 0.00537 **
## absdiff.Income 0.6398 0.3575 0 1.789 0.07356 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 23972 on 17292 degrees of freedom
## Residual Deviance: 1322 on 17284 degrees of freedom
##
## AIC: 1338 BIC: 1400 (Smaller is better. MC Std. Err. = 0.2814)Dependent variable: Transfer entropy is significant or not (binary), in other words, tract-tract PV adoption causal flow exists or not (with directionality).
Indep. variable:
* "mutual" means that a causal flow has reciprocity (A <-> B)
** "gwesp.OTP.fixed.0.01" is that if there is A -> B causal flow, it is
likely to have multiple transitting tracts indirectly shaping A -> B,
e.g., A -> C -> B & A -> D -> B if A -> B exists.
*** "absdiff" calculates absolute difference of an attribute in the causally
affecting and affected tracts in the homophily context. If the coeff. is
negative, tracts with similar attribute values tend to be causally
linked.- Bi-directional causal flows are observed more than expected in Vermont.
- Causal flows tend to share transits for indirect causal links.
- Similar housing conditions are important in creating causal connections in Seattle. Perhaps, urban areas are more sensitive to housing conditions.
- Causal flows emerge in two tracts with similar education levels and white rates.
- Income level tends to be different in sending and receiving tracts of causal flows. While Seattle did not have significant effects of income for senders or receivers alone, income heterophily is significant.
- Tract-tract diffusion in Seattle is more driven by homophily effects than sending or receiving effects.