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Dear Matthew,

Those two models are very different in both the underlying assumptions and the specifications. The first one is a SAR model which assumes that the errors are multivariate normal distributed, hence, no iid observations, and thus, the likelihood function is different from what you would observe in a plain OLS. Also, the spautolm includes the autocorrelation term when you specify listwd, so, if discrep_net_prop_more.W is your exposure terms, it means that you are including it twice but in the wrong way. Instead, you should type something like:

spautolm(formula = BLQFMHEDWM.W ~ 1, listw = w.list.trunc, 
    family = "SAR", zero.policy = TRUE)

For example. The autocorrelation term is the Lambda coefficient which is reported afterward.

The lm, on the other hand, runs an OLS model in which the errors are assumed to be iid making that type of model (including an exposure term) not valid as your estimates will be biased by construction (unless you are using a lagged exposure). A good reference on spatial econometrics is here:https://www.cairn.info/resume.php?ID_ARTICLE=REI_123_0019 (LeSage, 2008)

HIH

George G. Vega Yon
+1 (626) 381 8171
https://ggvy.cl

On Tue, Feb 20, 2018 at 2:43 PM, Meisel, Matthew <[log in to unmask]> wrote:
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Dear all,

My mentor has a large sociocentric network dataset (N = 1342) and I am trying to analyze the data using network autocorrelation models. When I run a model in R using the spautolm function and then I run the same model using the lm function, I get incredibly different results (the effects are significant but in different directions), and I have no idea on why these two methods would provide such vastly different results. See the models below. FYI, the predictor is dichotomous and the outcome is continuous. If you have any thoughts, please let me know, cause I do not know which results to trust.  

Best,
Matt

Call: spautolm(formula = BLQFMHEDWM.W ~ discrep_net_prop_more.W, listw = w.list.trunc, 
    family = "SAR", zero.policy = TRUE)

Residuals:
     Min       1Q   Median       3Q      Max 
-5.71857 -1.19085 -0.49541  0.55372 15.64806 

Coefficients: 
                        Estimate Std. Error z value  Pr(>|z|)
(Intercept)              1.64796    0.40402  4.0789 4.524e-05
discrep_net_prop_more.W -1.30912    0.18460 -7.0916 1.325e-12

Lambda: 0.83807 LR test value: 425.13 p-value: < 2.22e-16 
Numerical Hessian standard error of lambda: 0.030919 

Log likelihood: -2680.358 
ML residual variance (sigma squared): 5.0308, (sigma: 2.2429)
Number of observations: 1178 
Number of parameters estimated: 4 
AIC: 5368.7


Call: lm(formula = BLQFMHEDWM.W ~ discrep_net_prop_more.W, data = subject)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.2335 -1.7280 -1.7280  0.7665 18.2720 

Coefficients:
                        Estimate Std. Error t value Pr(>|t|)    
(Intercept)              1.72799    0.08878  19.465   <2e-16 ***
discrep_net_prop_more.W  0.50554    0.23578   2.144   0.0322 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.823 on 1176 degrees of freedom
Multiple R-squared:  0.003894, Adjusted R-squared:  0.003047 
F-statistic: 4.597 on 1 and 1176 DF,  p-value: 0.03223

--
Matthew K. Meisel, Ph.D.
Assistant Professor
Center for Alcohol and Addiction Studies
Department of Behavioral and Social Sciences
Brown University | School of Public Health
Box G-S121-4 Providence, RI 02903
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