estimate.default: Estimation of functional of parameters

In kkholst/lava: Latent Variable Models

Estimation of functional of parameters

Description

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

Usage

## 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:

\sqrt{n}(\widehat{\theta}-\theta) = \frac{1}{\sqrt{n}}\sum_{i=1}^n IC(Z_i; P) + o_p(1)

can be extracted with the IC method.

See Also

estimate.array

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,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)

kkholst/lava documentation built on Feb. 22, 2024, 4:07 p.m.