Voglio eseguire una regressione di quadrato minimo probit a due stadi in R. Qualcuno sa come fare? C'è qualche pacchetto là fuori? So che è possibile farlo usando Stata, quindi immagino sia possibile farlo con R.Minimo quadrato a due stadi in R
Si potrebbe voler essere più specifici quando si dice "probit-least-square-two-stage". Dato che ti riferisci a un programma Stata che implementa questo, suppongo tu stia parlando del pacchetto CDSIMEQ, che implementa la procedura Amemiya (1978) per il modello Heckit (a.k.a Tobia generalizzato, modello Tobit di tipo II, ecc.). Come ha detto Grant, systemfit farà un Tobit per te, ma non con due equazioni. Il pacchetto MicEcon aveva un Heckit (ma il pacchetto si è diviso così tante volte che non so dove sia ora).
Se si desidera quello che il CDSIMEQ fa, può essere facilmente implementato in R. Ho scritto una funzione che replica CDSIMEQ:
tspls <- function(formula1, formula2, data) {
# The Continous model
mf1 <- model.frame(formula1, data)
y1 <- model.response(mf1)
x1 <- model.matrix(attr(mf1, "terms"), mf1)
# The dicontionous model
mf2 <- model.frame(formula2, data)
y2 <- model.response(mf2)
x2 <- model.matrix(attr(mf2, "terms"), mf2)
# The matrix of all the exogenous variables
X <- cbind(x1, x2)
X <- X[, unique(colnames(X))]
J1 <- matrix(0, nrow = ncol(X), ncol = ncol(x1))
J2 <- matrix(0, nrow = ncol(X), ncol = ncol(x2))
for (i in 1:ncol(x1)) J1[match(colnames(x1)[i], colnames(X)), i] <- 1
for (i in 1:ncol(x2)) J2[match(colnames(x2)[i], colnames(X)), i] <- 1
# Step 1:
cat("\n\tNOW THE FIRST STAGE REGRESSION")
m1 <- lm(y1 ~ X - 1)
m2 <- glm(y2 ~ X - 1, family = binomial(link = "probit"))
print(summary(m1))
print(summary(m2))
yhat1 <- m1$fitted.values
yhat2 <- X %*% coef(m2)
PI1 <- m1$coefficients
PI2 <- m2$coefficients
V0 <- vcov(m2)
sigma1sq <- sum(m1$residuals^2)/m1$df.residual
sigma12 <- 1/length(y2) * sum(y2 * m1$residuals/dnorm(yhat2))
# Step 2:
cat("\n\tNOW THE SECOND STAGE REGRESSION WITH INSTRUMENTS")
m1 <- lm(y1 ~ yhat2 + x1 - 1)
m2 <- glm(y2 ~ yhat1 + x2 - 1, family = binomial(link = "probit"))
sm1 <- summary(m1)
sm2 <- summary(m2)
print(sm1)
print(sm2)
# Step 3:
cat("\tNOW THE SECOND STAGE REGRESSION WITH CORRECTED STANDARD ERRORS\n\n")
gamma1 <- m1$coefficients[1]
gamma2 <- m2$coefficients[1]
cc <- sigma1sq - 2 * gamma1 * sigma12
dd <- gamma2^2 * sigma1sq - 2 * gamma2 * sigma12
H <- cbind(PI2, J1)
G <- cbind(PI1, J2)
XX <- crossprod(X) # X'X
HXXH <- solve(t(H) %*% XX %*% H) # (H'X'XH)^(-1)
HXXVXXH <- t(H) %*% XX %*% V0 %*% XX %*% H # H'X'V0X'XH
Valpha1 <- cc * HXXH + gamma1^2 * HXXH %*% HXXVXXH %*% HXXH
GV <- t(G) %*% solve(V0) # G'V0^(-1)
GVG <- solve(GV %*% G) # (G'V0^(-1)G)^(-1)
Valpha2 <- GVG + dd * GVG %*% GV %*% solve(XX) %*% solve(V0) %*% G %*% GVG
ans1 <- coef(sm1)
ans2 <- coef(sm2)
ans1[,2] <- sqrt(diag(Valpha1))
ans2[,2] <- sqrt(diag(Valpha2))
ans1[,3] <- ans1[,1]/ans1[,2]
ans2[,3] <- ans2[,1]/ans2[,2]
ans1[,4] <- 2 * pt(abs(ans1[,3]), m1$df.residual, lower.tail = FALSE)
ans2[,4] <- 2 * pnorm(abs(ans2[,3]), lower.tail = FALSE)
cat("Continuous:\n")
print(ans1)
cat("Dichotomous:\n")
print(ans2)
}
Per confronto, si può replicare il campione da parte dell'autore di CDSIMEQ nella loro article about the package.
> library(foreign)
> cdsimeq <- read.dta("http://www.stata-journal.com/software/sj3-2/st0038/cdsimeq.dta")
> tspls(continuous ~ exog3 + exog2 + exog1 + exog4,
+ dichotomous ~ exog1 + exog2 + exog5 + exog6 + exog7,
+ data = cdsimeq)
NOW THE FIRST STAGE REGRESSION
Call:
lm(formula = y1 ~ X - 1)
Residuals:
Min 1Q Median 3Q Max
-1.885921 -0.438579 -0.006262 0.432156 2.133738
Coefficients:
Estimate Std. Error t value Pr(>|t|)
X(Intercept) 0.010752 0.020620 0.521 0.602187
Xexog3 0.158469 0.021862 7.249 8.46e-13 ***
Xexog2 -0.009669 0.021666 -0.446 0.655488
Xexog1 0.159955 0.021260 7.524 1.19e-13 ***
Xexog4 0.316575 0.022456 14.097 < 2e-16 ***
Xexog5 0.497207 0.021356 23.282 < 2e-16 ***
Xexog6 -0.078017 0.021755 -3.586 0.000352 ***
Xexog7 0.161177 0.022103 7.292 6.23e-13 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.6488 on 992 degrees of freedom
Multiple R-squared: 0.5972, Adjusted R-squared: 0.594
F-statistic: 183.9 on 8 and 992 DF, p-value: < 2.2e-16
Call:
glm(formula = y2 ~ X - 1, family = binomial(link = "probit"))
Deviance Residuals:
Min 1Q Median 3Q Max
-2.49531 -0.59244 0.01983 0.59708 2.41810
Coefficients:
Estimate Std. Error z value Pr(>|z|)
X(Intercept) 0.08352 0.05280 1.582 0.113692
Xexog3 0.21345 0.05678 3.759 0.000170 ***
Xexog2 0.21131 0.05471 3.862 0.000112 ***
Xexog1 0.45591 0.06023 7.570 3.75e-14 ***
Xexog4 0.39031 0.06173 6.322 2.57e-10 ***
Xexog5 0.75955 0.06427 11.818 < 2e-16 ***
Xexog6 0.85461 0.06831 12.510 < 2e-16 ***
Xexog7 -0.16691 0.05653 -2.953 0.003152 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 1386.29 on 1000 degrees of freedom
Residual deviance: 754.14 on 992 degrees of freedom
AIC: 770.14
Number of Fisher Scoring iterations: 6
NOW THE SECOND STAGE REGRESSION WITH INSTRUMENTS
Call:
lm(formula = y1 ~ yhat2 + x1 - 1)
Residuals:
Min 1Q Median 3Q Max
-2.32152 -0.53160 0.04886 0.53502 2.44818
Coefficients:
Estimate Std. Error t value Pr(>|t|)
yhat2 0.257592 0.021451 12.009 <2e-16 ***
x1(Intercept) 0.012185 0.024809 0.491 0.623
x1exog3 0.042520 0.026735 1.590 0.112
x1exog2 0.011854 0.026723 0.444 0.657
x1exog1 0.007773 0.028217 0.275 0.783
x1exog4 0.318636 0.028311 11.255 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.7803 on 994 degrees of freedom
Multiple R-squared: 0.4163, Adjusted R-squared: 0.4128
F-statistic: 118.2 on 6 and 994 DF, p-value: < 2.2e-16
Call:
glm(formula = y2 ~ yhat1 + x2 - 1, family = binomial(link = "probit"))
Deviance Residuals:
Min 1Q Median 3Q Max
-2.49610 -0.58595 0.01969 0.59857 2.41281
Coefficients:
Estimate Std. Error z value Pr(>|z|)
yhat1 1.26287 0.16061 7.863 3.75e-15 ***
x2(Intercept) 0.07080 0.05276 1.342 0.179654
x2exog1 0.25093 0.06466 3.880 0.000104 ***
x2exog2 0.22604 0.05389 4.194 2.74e-05 ***
x2exog5 0.12912 0.09510 1.358 0.174544
x2exog6 0.95609 0.07172 13.331 < 2e-16 ***
x2exog7 -0.37128 0.06759 -5.493 3.94e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 1386.29 on 1000 degrees of freedom
Residual deviance: 754.21 on 993 degrees of freedom
AIC: 768.21
Number of Fisher Scoring iterations: 6
NOW THE SECOND STAGE REGRESSION WITH CORRECTED STANDARD ERRORS
Continuous:
Estimate Std. Error t value Pr(>|t|)
yhat2 0.25759209 0.1043073 2.46955009 0.01369540
x1(Intercept) 0.01218500 0.1198713 0.10165068 0.91905445
x1exog3 0.04252006 0.1291588 0.32920764 0.74206810
x1exog2 0.01185438 0.1290754 0.09184073 0.92684309
x1exog1 0.00777347 0.1363643 0.05700519 0.95455252
x1exog4 0.31863627 0.1367881 2.32941597 0.02003661
Dichotomous:
Estimate Std. Error z value Pr(>|z|)
yhat1 1.26286574 0.7395166 1.7076909 0.0876937093
x2(Intercept) 0.07079775 0.2666447 0.2655134 0.7906139867
x2exog1 0.25092561 0.3126763 0.8025092 0.4222584495
x2exog2 0.22603717 0.2739307 0.8251618 0.4092797527
x2exog5 0.12911922 0.4822986 0.2677163 0.7889176766
x2exog6 0.95609385 0.2823662 3.3860070 0.0007091758
x2exog7 -0.37128221 0.3265478 -1.1369920 0.2555416141
ci sono diversi pacchetti disponibili in R per fare due minimi quadrati di stato. qui sono alcuni
fatemi sapere se questi servono il vostro scopo.
systemfit farà anche il trucco.
Grazie, ci proverò. Sembra adattarsi ai miei bisogni. –