compare2: Test Linear Hypotheses With Small Sample Correction

Description

Test Linear Hypotheses using Wald statistics in a latent variable model. Similar to lava::compare but with small sample correction.

Usage

compare2(
  object,
  linfct,
  rhs,
  robust,
  cluster,
  as.lava,
  F.test,
  conf.level,
  ...
)
# S3 method for lvmfit
compare2(
  object,
  linfct = NULL,
  rhs = NULL,
  robust = FALSE,
  cluster = NULL,
  as.lava = TRUE,
  F.test = TRUE,
  conf.level = 0.95,
  ssc = lava.options()$ssc,
  df = lava.options()$df,
  ...
)
# S3 method for lvmfit2
compare2(
  object,
  linfct = NULL,
  rhs = NULL,
  robust = FALSE,
  cluster = NULL,
  as.lava = TRUE,
  F.test = TRUE,
  conf.level = 0.95,
  ...
)
# S3 method for lvmfit2
compare(
  object,
  linfct = NULL,
  rhs = NULL,
  robust = FALSE,
  cluster = NULL,
  as.lava = TRUE,
  F.test = TRUE,
  conf.level = 0.95,
  ...
)

Value

If as.lava=TRUE an object of class htest. Otherwise a data.frame object.

Arguments

object: a lvmfit or lvmfit2 object (i.e. output of lava::estimate or lavaSearch2::estimate2).
linfct: [matrix or vector of character] the linear hypotheses to be tested. Same as the argument par of createContrast.
rhs: [vector] the right hand side of the linear hypotheses to be tested.
robust: [logical] should the robust standard errors be used instead of the model based standard errors?
cluster: [integer vector] the grouping variable relative to which the observations are iid.
as.lava: [logical] should the output be similar to the one return by lava::compare?
F.test: [logical] should a joint test be performed?
conf.level: [numeric 0-1] level of the confidence intervals.
...: additional argument passed to estimate2 when using a lvmfit object.
ssc: [character] method used to correct the small sample bias of the variance coefficients: no correction ("none"/FALSE/NA), correct the first order bias in the residual variance ("residual"), or correct the first order bias in the estimated coefficients "cox"). Only relevant when using a lvmfit object.
df: [character] method used to estimate the degree of freedoms of the Wald statistic: Satterthwaite "satterthwaite". Otherwise ("none"/FALSE/NA) the degree of freedoms are set to Inf. Only relevant when using a lvmfit object.

Details

The linfct argument and rhs specify the set of linear hypotheses to be tested. They can be written: $$ linfct * \theta = rhs $$ where $\theta$ is the vector of the model coefficients.
The par argument must contain expression(s) involving the model coefficients. For example "beta = 0" or c("-5*beta + alpha = 3","-alpha") are valid expressions if alpha and beta belong to the set of model coefficients. A contrast matrix and the right hand side will be generated inside the function.

When directly specified, the contrast matrix must contain as many columns as there are coefficients in the model (mean and variance coefficients). Each hypothesis correspond to a row in the contrast matrix.

The rhs vector should contain as many elements as there are row in the contrast matrix.

Examples

Run this code

#### simulate data ####
set.seed(10)
mSim <- lvm(Y~0.1*X1+0.2*X2)
categorical(mSim, labels = c("a","b","c")) <- ~X1
transform(mSim, Id~Y) <- function(x){1:NROW(x)}
df.data <- lava::sim(mSim, 1e2)

#### with lvm ####
m <- lvm(Y~X1+X2)
e.lvm <- estimate(m, df.data)

compare2(e.lvm, linfct = c("Y~X1b","Y~X1c","Y~X2"))
compare2(e.lvm, linfct = c("Y~X1b","Y~X1c","Y~X2"), robust = TRUE)