estimate.default function

Estimation of functional of parameters

Estimation of functional of parameters. Wald tests, robust standard errors, cluster robust standard errors, LRT (when f is not a function)...

## Default S3 method:
estimate(
  x = NULL,
  f = NULL,
  ...,
  data,
  id,
  iddata,
  stack = TRUE,
  average = FALSE,
  subset,
  score.deriv,
  level = 0.95,
  IC = robust,
  type = c("robust", "df", "mbn"),
  keep,
  use,
  regex = FALSE,
  ignore.case = FALSE,
  contrast,
  null,
  vcov,
  coef,
  robust = TRUE,
  df = NULL,
  print = NULL,
  labels,
  label.width,
  only.coef = FALSE,
  back.transform = NULL,
  folds = 0,
  cluster,
  R = 0,
  null.sim
)

Arguments

• x: model object (glm, lvmfit, ...)
• f: transformation of model parameters and (optionally) data, or contrast matrix (or vector)
• ...: additional arguments to lower level functions
• data: data.frame
• id: (optional) id-variable corresponding to ic decomposition of model parameters.
• iddata: (optional) id-variable for 'data'
• stack: if TRUE (default) the i.i.d. decomposition is automatically stacked according to 'id'
• average: if TRUE averages are calculated
• subset: (optional) subset of data.frame on which to condition (logical expression or variable name)
• score.deriv: (optional) derivative of mean score function
• level: level of confidence limits
• IC: if TRUE (default) the influence function decompositions are also returned (extract with IC method)
• type: type of small-sample correction
• keep: (optional) index of parameters to keep from final result
• use: (optional) index of parameters to use in calculations
• regex: If TRUE use regular expression (perl compatible) for keep, use arguments
• ignore.case: Ignore case-sensitiveness in regular expression
• contrast: (optional) Contrast matrix for final Wald test
• null: (optional) null hypothesis to test
• vcov: (optional) covariance matrix of parameter estimates (e.g. Wald-test)
• coef: (optional) parameter coefficient
• robust: if TRUE robust standard errors are calculated. If FALSE p-values for linear models are calculated from t-distribution
• df: degrees of freedom (default obtained from 'df.residual')
• print: (optional) print function
• labels: (optional) names of coefficients
• label.width: (optional) max width of labels
• only.coef: if TRUE only the coefficient matrix is return
• back.transform: (optional) transform of parameters and confidence intervals
• folds: (optional) aggregate influence functions (divide and conquer)
• cluster: (obsolete) alias for 'id'.
• R: Number of simulations (simulated p-values)
• null.sim: Mean under the null for simulations

Details

influence function decomposition of estimator $\widehat{\theta}$ based on data $Z_1,\ldots,Z_n$:

can be extracted with the IC method.

Examples

## Simulation from logistic regression model
m <- lvm(y~x+z);
distribution(m,y~x) <- binomial.lvm("logit")
d <- sim(m,1000)
g <- glm(y~z+x,data=d,family=binomial())
g0 <- glm(y~1,data=d,family=binomial())

## LRT
estimate(g,g0)

## Plain estimates (robust standard errors)
estimate(g)

## Testing contrasts
estimate(g,null=0)
estimate(g,rbind(c(1,1,0),c(1,0,2)))
estimate(g,rbind(c(1,1,0),c(1,0,2)),null=c(1,2))
estimate(g,2:3) ## same as cbind(0,1,-1)
estimate(g,as.list(2:3)) ## same as rbind(c(0,1,0),c(0,0,1))
## Alternative syntax
estimate(g,"z","z"-"x",2*"z"-3*"x")
estimate(g,"?")  ## Wildcards
estimate(g,"*Int*","z")
estimate(g,"1","2"-"3",null=c(0,1))
estimate(g,2,3)

## Usual (non-robust) confidence intervals
estimate(g,robust=FALSE)

## Transformations
estimate(g,function(p) p[1]+p[2])

## Multiple parameters
e <- estimate(g,function(p) c(p[1]+p[2], p[1]*p[2]))
e
vcov(e)

## Label new parameters
estimate(g,function(p) list("a1"=p[1]+p[2], "b1"=p[1]*p[2]))
##'
## Multiple group
m <- lvm(y~x)
m <- baptize(m)
d2 <- d1 <- sim(m,50,seed=1)
e <- estimate(list(m,m),list(d1,d2))
estimate(e) ## Wrong
ee <- estimate(e, id=rep(seq(nrow(d1)), 2)) ## Clustered
ee
estimate(lm(y~x,d1))

## Marginalize
f <- function(p,data)
  list(p0=lava:::expit(p["(Intercept)"] + p["z"]*data[,"z"]),
       p1=lava:::expit(p["(Intercept)"] + p["x"] + p["z"]*data[,"z"]))
e <- estimate(g, f, average=TRUE)
e
estimate(e,diff)
estimate(e,cbind(1,1))

## Clusters and subset (conditional marginal effects)
d$id <- rep(seq(nrow(d)/4),each=4)
estimate(g,function(p,data)
         list(p0=lava:::expit(p[1] + p["z"]*data[,"z"])),
         subset=d$z>0, id=d$id, average=TRUE)

## More examples with clusters:
m <- lvm(c(y1,y2,y3)~u+x)
d <- sim(m,10)
l1 <- glm(y1~x,data=d)
l2 <- glm(y2~x,data=d)
l3 <- glm(y3~x,data=d)

## Some random id-numbers
id1 <- c(1,1,4,1,3,1,2,3,4,5)
id2 <- c(1,2,3,4,5,6,7,8,1,1)
id3 <- seq(10)

## Un-stacked and stacked i.i.d. decomposition
IC(estimate(l1,id=id1,stack=FALSE))
IC(estimate(l1,id=id1))

## Combined i.i.d. decomposition
e1 <- estimate(l1,id=id1)
e2 <- estimate(l2,id=id2)
e3 <- estimate(l3,id=id3)
(a2 <- merge(e1,e2,e3))

## If all models were estimated on the same data we could use the
## syntax:
## Reduce(merge,estimate(list(l1,l2,l3)))

## Same:
IC(a1 <- merge(l1,l2,l3,id=list(id1,id2,id3)))

IC(merge(l1,l2,l3,id=TRUE)) # one-to-one (same clusters)
IC(merge(l1,l2,l3,id=FALSE)) # independence

## Monte Carlo approach, simple trend test example

m <- categorical(lvm(),~x,K=5)
regression(m,additive=TRUE) <- y~x
d <- simulate(m,100,seed=1,'y~x'=0.1)
l <- lm(y~-1+factor(x),data=d)

f <- function(x) coef(lm(x~seq_along(x)))[2]
null <- rep(mean(coef(l)),length(coef(l)))
##  just need to make sure we simulate under H0: slope=0
estimate(l,f,R=1e2,null.sim=null)

estimate(l,f)

See Also

estimate.array