netpanel: An R Package that Contains Maximum Likelihood Estimation Routines for Panel Network Autocorrelation Models

The netpanel package contains maximum likelihood estimation routines to fit panel network autocorrelation models (PNAMs) with time-varying social adjacency matrices. The package contains functionality for (1) fixed and random effects PNAMs, (2) dynamic PNAMs that include time lags of the outcome and networks, and (3) the estimation of network mixed effects models where, in addition to the lag of the outcome, the time-varying residuals are assumed to exhibit network autocorrelation. Importantly, the package allows for multiple network lags to be fitted simultaneously. Please see the list of below references for more information on panel network (spatial) autocorrelation models. For generality, a panel network autocorrelation model is a linear regression model that takes the following form:

$$Y_t = \lambda_1 W^{t}_{1}Y_t + \cdots + \lambda_k W^{t}_{k}Y_t + X_t\beta + v_t, \ \ t = 1,2,\cdots,T $$

where $Y_t$ is the outcome vector for $N$ actors at time $t$, $\lambda_k W^{t}_{k}Y_t$ is the network autocorrelation term for the $k^{th}$ social network at time $t$, $X_t$ are the set of exogenous time-varying (and invariant) regressors. Moreover, the broad definition of the time-varying error term $v_t$ is:

$$v_t = \mu_N + e_t,\ \ t = 1,2,\cdots,T $$

where $\mu_N$ are time-invariant unit-specific unobserved factors thought to explain $Y_t$ and $e_t$ are the time- and unit-varying unobserved factors.

Authors

Kevin A. Carson

• Author & Maintainer
• PhD Candidate at the University of Arizona School of Sociology
• Email: kacarson@arizona.edu
• Website: https://kevincarson.github.io/

Installation

You can install the developmental version of netpanel from GitHub with:

remotes::install_github("kevinCarson/netpanel")

The netpanel Package API

The netpanel package API primarily works through the wrapper function mlpnam(). The mlpnam() function returns an S3 object of class pnam that stores the relevant results of the fitted PNAM. The full set of functions (including user-helper S3 methods) are:

• mlpnam(): fits a panel network autocorrelation model to an empirical panel network dataset via Maximum Likelihood Estimation.
• netimpacts(): computes the direct, indirect, and total network impacts for each included regressor from a fitted pnam S3 object.
• coef.pnam(): extracts the vector of ML parameter estimates from a fitted pnam S3 object.
• vcov.pnam(): extracts the asymptotic variance-covariance matrix from a fitted pnam S3 object.
• logLik.pnam(): extracts the estimated log-likelihood from a fitted pnam S3 object.
• residuals.pnam(): extracts the model residuals from a fitted pnam S3 object.
• fitted.pnam(): extracts the linear and network regression fitted values from a fitted pnam S3 object.

Fitting a Random Effects Panel Network Autocorrelation Model with netpanel

Importantly, the netpanel package includes a set of simulated pseudo data objects for users to start fitting panel network autocorrelation models. Below, we rely upon them to provide a brief example of how the netpanel package fits these types of models.

library(netpanel)
data("net1", package = "netpanel") #the first panel network
data("net2", package = "netpanel") #the second panel network
data("net3", package = "netpanel") #the third panel network
data("simulated.data", package = "netpanel") #the simulated variables 

# a random effects panel network autocorrelation model
re.pnam <- mlpnam(Y~x1+x2+x3, net.formula = ~ net1 + net2,
               data =  simulated.data, time = ~panel,
               actor = ~unit, model = "random")

summary(re.pnam) 
#> Maximum Likelihood Panel Network Autocorrelation Model with Unit-Level Random Effects
#> 
#> Call:
#> mlpnam(reg.formula = Y ~ x1 + x2 + x3, net.formula = ~net1 + 
#>     net2, data = simulated.data, time = ~panel, actor = ~unit, 
#>     model = "random")
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -4.48611 -0.93835 -0.08678  0.89373  4.23752 
#> 
#> Panel error variance components:
#>                     sd     var
#> idiosyncratic: 0.90180 0.81324
#> unit-specific: 1.06094 1.12560
#> theta: 1.3841 (SE: 0.31323; p= 1e-05)
#> icc: 0.58055
#> 
#> Network autocorrelation parameters:
#>      Estimate Std. Error z value  Pr(>|z|)    
#> net1  0.26437    0.05388  4.9067 < 2.2e-16 ***
#> net2  0.29327    0.06024  4.8684 < 2.2e-16 ***
#> 
#> ML regression coefficients:
#>             Estimate Std. Error z value  Pr(>|z|)    
#> (Intercept)  9.93222    0.16010  62.037 < 2.2e-16 ***
#> x1           0.85819    0.04277  20.068 < 2.2e-16 ***
#> x2          -1.13678    0.08582 -13.246 < 2.2e-16 ***
#> x3           1.99977    0.04052  49.356 < 2.2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Model fit information:
#>  -> number of observations: 500; N: 50; T: 10
#>  -> parameters estimated: 8 
#>  -> log-likehoood: -901.1132 (df=492); AIC: 1818.226; BIC: 1851.943
#>  -> residual SD: 0.9018
#>  -> optim convergence: yes
#>  -> search iterations: 15
#>  -> largest eigenvalue of rho*W: 0.5576419

impacts <- netimpacts(re.pnam) #extracting the network impacts

print(impacts) 
#>   Regressor   Direct Indirect    Total
#> 1        x1  0.87035  1.06970  1.94004
#> 2        x2 -1.15288 -1.41694 -2.56982
#> 3        x3  2.02809  2.49262  4.52071

We can extend the above model by fitting a mixed network random effects panel autocorrelation with netpanel that allows for the time-varying residuals to be autocorrelated across the network ties.

# a random effects network mixed effects panel autocorrelation model
re.pnam.mixed <- mlpnam(Y~x1+x2+x3, net.formula = ~ net1 + net2,
               data =  simulated.data, time = ~panel,
               actor = ~unit, model = "random",
               errors = "autocorrelated",
               autocorrelated.network = net3)

summary(re.pnam.mixed) 
#> Maximum Likelihood Panel Network Autocorrelation Model with Unit-Level Random Effects
#> 
#> Call:
#> mlpnam(reg.formula = Y ~ x1 + x2 + x3, net.formula = ~net1 + 
#>     net2, data = simulated.data, time = ~panel, actor = ~unit, 
#>     model = "random", errors = "autocorrelated", autocorrelated.network = net3)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -4.48412 -0.91269 -0.07685  0.93722  4.18802 
#> 
#> Panel error variance components:
#>                     sd     var
#> idiosyncratic: 0.89532 0.80159
#> unit-specific: 1.05886 1.12118
#> theta: 1.3987 (SE: 0.31596; p= 1e-05)
#> icc: 0.58311
#> 
#> Network autocorrelation parameters:
#>      Estimate Std. Error z value Pr(>|z|)    
#> net1  0.25753    0.05519  4.6661  < 2e-16 ***
#> net2  0.25198    0.06829  3.6899  0.00022 ***
#> 
#> Network error parameters:
#>        Estimate Std. Error z value Pr(>|z|)   
#> lambda  0.35450    0.13641  2.5989  0.00935 **
#> 
#> ML regression coefficients:
#>             Estimate Std. Error z value  Pr(>|z|)    
#> (Intercept) 10.96107    0.16641  65.869 < 2.2e-16 ***
#> x1           0.86139    0.04237  20.331 < 2.2e-16 ***
#> x2          -1.14165    0.08430 -13.543 < 2.2e-16 ***
#> x3           1.99746    0.04015  49.756 < 2.2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Model fit information:
#>  -> number of observations: 500; N: 50; T: 10
#>  -> parameters estimated: 9 
#>  -> log-likehoood: -898.1102 (df=491); AIC: 1814.22; BIC: 1852.152
#>  -> residual SD: 0.89532
#>  -> optim convergence: yes
#>  -> search iterations: 17
#>  -> largest eigenvalue of rho*W: 0.5095095

Questions, Comments, or Suggestions!

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