Comparison fits
- Example from the ivtools
ivglm()
helpfile. First simulate some example data.
set.seed(12345)
n <- 5000
psi0 <- 0.5
psi1 <- 0.2
Z <- rbinom(n, 1, 0.5)
X <- rbinom(n, 1, 0.7*Z + 0.2*(1 - Z))
m0 <- plogis(1 + 0.8*X - 0.39*Z)
Y <- rbinom(n, 1, plogis(psi0*X + log(m0/(1 - m0))))
dat <- data.frame(Z, X, Y)
- Comparison fit using
msmm().
fit02 <- msmm(Y ~ X | Z, data = dat)
summary(fit02)
#>
#> Estimation method: gmm
#>
#> GMM fit summary:
#>
#> Call:
#> gmm::gmm(g = msmmMoments, x = dat, t0 = t0, vcov = "iid")
#>
#>
#> Method: twoStep
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> Theta[1] 7.4993e-01 1.2332e-02 6.0810e+01 0.0000e+00
#> Theta[2] 1.0198e-01 2.8219e-02 3.6140e+00 3.0156e-04
#>
#> J-Test: degrees of freedom is 0
#> J-test P-value
#> Test E(g)=0: 3.31877269935166e-06 *******
#>
#> #############
#> Information related to the numerical optimization
#> Convergence code = 0
#> Function eval. = 61
#> Gradian eval. = NA
#>
#> E[Y(0)] with 95% CI:
#> 0.025 0.975
#> 0.7499 0.7258 0.7741
#>
#> Causal risk ratio with 95% CI:
#> CRR 0.025 0.975
#> X 1.107 1.048 1.17
- Comparison fit using the alternative GMM moment conditions.
fit03 <- msmm(Y ~ X | Z, data = dat, estmethod = "gmmalt")
summary(fit03)
#>
#> Estimation method: gmmalt
#>
#> GMM fit summary:
#>
#> Call:
#> gmm::gmm(g = msmmAltMoments, x = dat, t0 = t0, vcov = "iid")
#>
#>
#> Method: twoStep
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> Theta[1] -2.8759e-01 1.6444e-02 -1.7489e+01 1.7356e-68
#> Theta[2] 1.0173e-01 2.8217e-02 3.6053e+00 3.1178e-04
#>
#> J-Test: degrees of freedom is 0
#> J-test P-value
#> Test E(g)=0: 3.75832932725745e-06 *******
#>
#> #############
#> Information related to the numerical optimization
#> Convergence code = 0
#> Function eval. = 55
#> Gradian eval. = NA
#>
#> E[Y(0)] with 95% CI:
#> 0.025 0.975
#> 0.7501 0.7263 0.7746
#>
#> Causal risk ratio with 95% CI:
#> CRR 0.025 0.975
#> X 1.107 1.048 1.17
- Comparison fit using transformed variables using two-stage least
squares.
fit04 <- msmm(Y ~ X | Z, data = dat, estmethod = "tsls")
summary(fit04)
#>
#> Estimation method: tsls
#>
#> Stage 1 summary:
#>
#> Call:
#> stats::lm(formula = exposure ~ z)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.6206 -0.1873 -0.1873 0.3794 0.8127
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.187272 0.008878 21.09 <2e-16 ***
#> z 0.433336 0.012474 34.74 <2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.441 on 4998 degrees of freedom
#> Multiple R-squared: 0.1945, Adjusted R-squared: 0.1943
#> F-statistic: 1207 on 1 and 4998 DF, p-value: < 2.2e-16
#>
#> TSLS fit summary:
#>
#> Call:
#> ivreg::ivreg(formula = outcome ~ exposure | z)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.7500 0.1532 0.1532 0.2500 0.2500
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.75000 0.01173 63.95 <2e-16 ***
#> exposure -0.90315 0.02545 -35.49 <2e-16 ***
#>
#> Diagnostic tests:
#> df1 df2 statistic p-value
#> Weak instruments 1 4998 1206.9 <2e-16 ***
#> Wu-Hausman 1 4997 147.1 <2e-16 ***
#> Sargan 0 NA NA NA
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.3898 on 4998 degrees of freedom
#> Multiple R-Squared: 0.3569, Adjusted R-squared: 0.3567
#> Wald test: 1260 on 1 and 4998 DF, p-value: < 2.2e-16
#>
#>
#> E[Y(0)] with 95% CI:
#> 2.5 % 97.5 %
#> 0.750 0.727 0.773
#>
#> Causal risk ratio with 95% CI:
#> [1] 1.107 1.048 1.170
- Comparison fit using the alternative transformed variables approach
using two-stage least squares.
fit05 <- msmm(Y ~ X | Z, data = dat, estmethod = "tslsalt")
summary(fit05)
#>
#> Estimation method: tslsalt
#>
#> Stage 1 summary:
#>
#> Call:
#> stats::lm(formula = exposure ~ z)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.5809 -0.1895 -0.1895 0.4191 0.8105
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.580867 0.008959 64.84 <2e-16 ***
#> z -0.391369 0.012587 -31.09 <2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.445 on 4998 degrees of freedom
#> Multiple R-squared: 0.1621, Adjusted R-squared: 0.1619
#> F-statistic: 966.8 on 1 and 4998 DF, p-value: < 2.2e-16
#>
#> TSLS fit summary:
#>
#> Call:
#> ivreg::ivreg(formula = outcome ~ exposure | z)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.8304 0.1696 0.1696 0.2768 0.2768
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.83043 0.01341 61.94 <2e-16 ***
#> exposure -1.10723 0.03120 -35.49 <2e-16 ***
#>
#> Diagnostic tests:
#> df1 df2 statistic p-value
#> Weak instruments 1 4998 966.8 <2e-16 ***
#> Wu-Hausman 1 4997 354.2 <2e-16 ***
#> Sargan 0 NA NA NA
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.4316 on 4998 degrees of freedom
#> Multiple R-Squared: 0.2282, Adjusted R-squared: 0.2281
#> Wald test: 1260 on 1 and 4998 DF, p-value: < 2.2e-16
#>
#>
#> Causal risk ratio with 95% CI:
#> [1] 1.107 1.048 1.170