Bivariate Probit model

Usage

biprobit(
  x,
  data,
  id,
  rho = ~1,
  num = NULL,
  strata = NULL,
  eqmarg = TRUE,
  indep = FALSE,
  weights = NULL,
  weights.fun = function(x) ifelse(any(x <= 0), 0, max(x)),
  randomeffect = FALSE,
  vcov = "robust",
  pairs.only = FALSE,
  allmarg = !is.null(weights),
  control = list(trace = 0),
  messages = 1,
  constrain = NULL,
  table = pairs.only,
  p = NULL,
  ...
)

Arguments

x: formula (or vector)
data: data.frame
id: The name of the column in the dataset containing the cluster id-variable.
rho: Formula specifying the regression model for the dependence parameter
num: Optional name of order variable
strata: Strata
eqmarg: If TRUE same marginals are assumed (exchangeable)
indep: Independence
weights: Weights
weights.fun: Function defining the bivariate weight in each cluster
randomeffect: If TRUE a random effect model is used (otherwise correlation parameter is estimated allowing for both negative and positive dependence)
vcov: Type of standard errors to be calculated
pairs.only: Include complete pairs only?
allmarg: Should all marginal terms be included
control: Control argument parsed on to the optimization routine. Starting values may be parsed as 'start'.
messages: Control amount of messages shown
constrain: Vector of parameter constraints (NA where free). Use this to set an offset.
table: Type of estimation procedure
p: Parameter vector p in which to evaluate log-Likelihood and score function
...: Optional arguments

Examples

data(prt)
prt0 <- subset(prt,country=="Denmark")
a <- biprobit(cancer~1+zyg, ~1+zyg, data=prt0, id="id")
predict(a, newdata=lava::Expand(prt, zyg=c("MZ")))
#>           p11        p10        p01       p00         p1         p2       mu1
#> 1 0.005649701 0.01034772 0.01034772 0.9736549 0.01599742 0.01599742 -2.144475
#>         mu2       rho parameter zyg
#> 1 -2.144475 0.7547259         1  MZ
## b <- biprobit(cancer~1+zyg, ~1+zyg, data=prt0, id="id",pairs.only=TRUE)
## predict(b,newdata=lava::Expand(prt,zyg=c("MZ","DZ")))

 ## Reduce Ex.Timings
n <- 2e3
x <- sort(runif(n, -1, 1))
y <- rmvn(n, c(0,0), rho=cbind(tanh(x)))>0
d <- data.frame(y1=y[,1], y2=y[,2], x=x)
dd <- fast.reshape(d)

a <- biprobit(y~1+x,rho=~1+x,data=dd,id="id")
summary(a, mean.contrast=c(1,.5), cor.contrast=c(1,.5))
#> 
#>                 Estimate    Std.Err       Z p-value    
#> (Intercept)   -0.0092239  0.0197080 -0.4680  0.6398    
#> x              0.0101193  0.0313670  0.3226  0.7470    
#> r:(Intercept) -0.0229627  0.0383073 -0.5994  0.5489    
#> r:x            0.9894711  0.0692001 14.2987  <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> logLik: -2651.885  mean(score^2): 1.394e-05 
#>     n pairs 
#>  4000  2000 
#> 
#> Contrast:
#> 	Dependence    [(Intercept)] + 0.5[x] 
#> 	Mean          [(Intercept)] + 0.5[x] 
#> 
#>                         Estimate 2.5%    97.5%  
#> Rel.Recur.Risk          1.29171  1.22694 1.35649
#> OR                      3.29799  2.55557 4.25610
#> Tetrachoric correlation 0.43963  0.35367 0.51823
#>                                                 
#> Concordance             0.32079  0.29429 0.34849
#> Casewise Concordance    0.64371  0.60960 0.67642
#> Marginal                0.49834  0.47536 0.52132
with(predict(a,data.frame(x=seq(-1,1,by=.1))), plot(p00~x,type="l"))


pp <- predict(a,data.frame(x=seq(-1,1,by=.1)),which=c(1))
plot(pp[,1]~pp$x, type="l", xlab="x", ylab="Concordance", lwd=2, xaxs="i")
lava::confband(pp$x,pp[,2],pp[,3],polygon=TRUE,lty=0,col=lava::Col(1))


pp <- predict(a,data.frame(x=seq(-1,1,by=.1)),which=c(9)) ## rho
plot(pp[,1]~pp$x, type="l", xlab="x", ylab="Correlation", lwd=2, xaxs="i")
lava::confband(pp$x,pp[,2],pp[,3],polygon=TRUE,lty=0,col=lava::Col(1))
with(pp, lines(x,tanh(-x),lwd=2,lty=2))

xp <- seq(-1,1,length.out=6); delta <- mean(diff(xp))
a2 <- biprobit(y~1+x,rho=~1+I(cut(x,breaks=xp)),data=dd,id="id")
pp2 <- predict(a2,data.frame(x=xp[-1]-delta/2),which=c(9)) ## rho
lava::confband(pp2$x,pp2[,2],pp2[,3],center=pp2[,1])





## Time
if (FALSE) { # \dontrun{
    a <- biprobit.time(cancer~1, rho=~1+zyg, id="id", data=prt, eqmarg=TRUE,
                       cens.formula=Surv(time,status==0)~1,
                       breaks=seq(75,100,by=3),fix.censweights=TRUE)

    a <- biprobit.time2(cancer~1+zyg, rho=~1+zyg, id="id", data=prt0, eqmarg=TRUE,
                       cens.formula=Surv(time,status==0)~zyg,
                       breaks=100)

    #a1 <- biprobit.time2(cancer~1, rho=~1, id="id", data=subset(prt0,zyg=="MZ"), eqmarg=TRUE,
    #                   cens.formula=Surv(time,status==0)~1,
    #                   breaks=100,pairs.only=TRUE)

    #a2 <- biprobit.time2(cancer~1, rho=~1, id="id", data=subset(prt0,zyg=="DZ"), eqmarg=TRUE,
    #                    cens.formula=Surv(time,status==0)~1,
    #                    breaks=100,pairs.only=TRUE)
} # }