Zelig 5 workflow overview

All models in Zelig 5 can be estimated and results explored presented using a five simple steps:

• Initialise the Zelig object, e.g with z.out <- zls$new() for a least squares model. Then populate the object with:

• zelig to estimate the parameters,

• setx to set fitted values for which we want to find quantities of interest,

• sim to simulate the quantities of interest,

• graph to plot the simulation results.

z5 <- zls$new()
z5$zelig(Y ~ X1 + X ~ X, weights = w, data = mydata)
z5$setx()
z5$sim()
z5$graph()

z.out <- zelig(Y ~ X1 + X2, model = "ls", weights = w, data = mydata)
x.out <- setx(z.out)
s.out <- sim(z.out, x = x.out)
plot(s.out)

Zelig 5 Quickstart Guide

Let’s walk through an example. This example uses the swiss dataset. It contains data on fertility and socioeconomic factors in Switzerland’s 47 French-speaking provinces in 1888 (Mosteller and Tukey, 1977, 549-551). We will model the effect of education on fertility, where education is measured as the percent of draftees with education beyond primary school and fertility is measured using the common standardized fertility measure (see Muehlenbein (2010, 80-81) for details).

Installing and Loading Zelig

If you haven’t already done so, open your R console and install Zelig:

install.packages('Zelig')

Alternatively you can install the development version with:

devtools::install_github('IQSS/Zelig')

Once Zelig is installed, load it:

library(Zelig)

Building Models

Let’s assume we want to estimate the effect of education on fertility. Since fertility is a continuous variable, least squares is an appropriate model choice. We first create a Zelig least squares object:

# initialize Zelig5 least squares object
z5 <- zls$new()

To estimate our model, we call the zelig() method, which is a function that is internal to the Zelig object. We pass the zelig() method two arguments: equation and data:

# estimate ls model
z5$zelig(Fertility ~ Education, data = swiss)

# model summary
summary(z5)

## Model: 
## 
## Call:
## z5$zelig(formula = Fertility ~ Education, data = swiss)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -17.036  -6.711  -1.011   9.526  19.689 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)  79.6101     2.1041  37.836  < 2e-16
## Education    -0.8624     0.1448  -5.954 3.66e-07
## 
## Residual standard error: 9.446 on 45 degrees of freedom
## Multiple R-squared:  0.4406, Adjusted R-squared:  0.4282 
## F-statistic: 35.45 on 1 and 45 DF,  p-value: 3.659e-07
## 
## Next step: Use 'setx' method

The -0.8624 coefficient on education suggests a negative relationship between the education of a province and its fertility rate. More precisely, for every one percent increase in draftees educated beyond primary school, the fertility rate of the province decreases 0.8624 units. To help us better interpret this finding, we may want other quantities of interest, such as expected values or first differences. Zelig makes this simple by automating the translation of model estimates into interpretable quantities of interest using Monte Carlo simulation methods (see King, Tomz, and Wittenberg (2000) for more information). For example, let’s say we want to examine the effect of increasing the percent of draftees educated from 5 to 15. To do so, we set our predictor value using the setx() method:

# set education to 5
z5$setx(Education = 5)

# set education to 15
z5$setx1(Education = 15)

# model summary
summary(z5)

## setx:
##   (Intercept) Education
## 1           1         5
## setx1:
##   (Intercept) Education
## 1           1        15
## 
## Next step: Use 'sim' method

After setting our predictor value, we simulate using the sim() method:

# run simulations and estimate quantities of interest
z5$sim()

# model summary
summary(z5)

## 
##  sim x :
##  -----
## ev
##       mean       sd      50%     2.5%    97.5%
## 1 75.27756 1.698201 75.31306 72.03171 78.58321
## pv
##          mean       sd      50%     2.5%    97.5%
## [1,] 75.19193 9.294041 75.14807 56.93787 92.88346
## 
##  sim x1 :
##  -----
## ev
##       mean       sd      50%    2.5%    97.5%
## 1 66.65694 1.549874 66.67741 63.5882 69.59176
## pv
##          mean       sd     50%     2.5%    97.5%
## [1,] 66.43407 8.985926 66.6938 48.81676 83.27413
## fd
##       mean       sd       50%      2.5%     97.5%
## 1 -8.62062 1.498029 -8.641185 -11.50061 -5.776213

At this point, we’ve estimated a model, set the predictor value, and estimated easily interpretable quantities of interest. The summary() method shows us our quantities of interest, namely, our expected and predicted values at each level of education, as well as our first differences–the difference in expected values at the set levels of education.

Visualizations

Zelig’s graph() method plots the estimated quantities of interest:

z5$graph()

We can also simulate and plot simulations from ranges of simulated values. For example, first use the setrange method to set a range of fitted values for one of the covariates and draw simulations as before:

z5 <- zls$new()
z5$zelig(Fertility ~ Education, data = swiss)

# set Education to range from 5 to 15 at single integer increments
z5$setrange(Education = 5:15)

# run simulations and estimate quantities of interest
z5$sim()

Then use the graph() method as before:

z5$graph()