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Statistical Inference for Derived Parameters

BIFIE.derivedParameters.Rd

This function performs statistical for derived parameters for objects of classes BIFIE.by, BIFIE.correl, BIFIE.crosstab, BIFIE.freq, BIFIE.linreg, BIFIE.logistreg and BIFIE.univar.

Usage

BIFIE.derivedParameters( BIFIE.method, derived.parameters, type=NULL)

# S3 method for class 'BIFIE.derivedParameters'
summary(object,digits=4,...)

# S3 method for class 'BIFIE.derivedParameters'
coef(object,...)

# S3 method for class 'BIFIE.derivedParameters'
vcov(object,...)

Arguments

BIFIE.method

Object of classes BIFIE.by, BIFIE.correl, BIFIE.crosstab, BIFIE.freq, BIFIE.linreg, BIFIE.logistreg or BIFIE.univar (see parnames in the Output of these methods for saved parameters)

derived.parameters

List with R formulas for derived parameters (see Examples for specification)

type

Only applies to BIFIE.correl. In case of type="cov" covariances instead of correlations are used for derived parameters.

object

Object of class BIFIE.derivedParameters

digits

Number of digits for rounding decimals in output

...

Further arguments to be passed

Details

The distribution of derived parameters is derived by the direct calculation using original resampled parameters.

Value

A list with following entries

stat

Data frame with statistics

coef

Estimates of derived parameters

vcov

Covariance matrix of derived parameters

parnames

Parameter names

res_wald

Output of Wald test (global test regarding all parameters)

...

More values

See also

See also BIFIE.waldtest for multi-parameter tests.

See car::deltaMethod for the Delta method assuming that the multivariate distribution of the parameters is asymptotically normal.

Examples

#############################################################################
# EXAMPLE 1: Imputed TIMSS dataset
#            Inference for correlations and derived parameters
#############################################################################

data(data.timss1)
data(data.timssrep)

# create BIFIE.dat object
bdat <- BIFIEsurvey::BIFIE.data( data.list=data.timss1, wgt=data.timss1[[1]]$TOTWGT,
           wgtrep=data.timssrep[, -1 ] )
#> +++ Generate BIFIE.data object
#> |*****|
#> |-----|

# compute correlations
res1 <- BIFIEsurvey::BIFIE.correl( bdat,
            vars=c("ASSSCI", "ASMMAT", "books", "migrant" )  )
#> |*****|
#> |-----|
summary(res1)
#> ------------------------------------------------------------
#> BIFIEsurvey 3.8.0 () 
#> 
#> Function 'BIFIE.correl'
#> 
#> Call:
#> BIFIEsurvey::BIFIE.correl(BIFIEobj = bdat, vars = c("ASSSCI", 
#>     "ASMMAT", "books", "migrant"))
#> 
#> Date of Analysis: 2026-01-11 08:35:24.702476 
#> Time difference of 0.2890172 secs
#> Computation time: 0.2890172 
#> 
#> Multiply imputed dataset
#> 
#> Number of persons = 4668 
#> Number of imputed datasets = 5 
#> Number of Jackknife zones per dataset = 75 
#> Fay factor = 1 
#> 
#> Statistical Inference for Correlations 
#>     var1    var2 Ncases  Nweight     cor cor_SE      t     df p cor_fmi
#> 2 ASSSCI  ASMMAT   4668 78332.99  0.8292 0.0090  92.62  13.43 0  0.5457
#> 3 ASSSCI   books   4668 78332.99  0.3739 0.0217  17.22 962.93 0  0.0645
#> 4 ASSSCI migrant   4668 78332.99 -0.3402 0.0217 -15.65 354.02 0  0.1063
#> 6 ASMMAT   books   4668 78332.99  0.3379 0.0214  15.78 270.79 0  0.1215
#> 7 ASMMAT migrant   4668 78332.99 -0.2287 0.0237  -9.64 359.64 0  0.1055
#> 9  books migrant   4668 78332.99 -0.2537 0.0209 -12.13    Inf 0  0.0445
#>   cor_VarMI cor_VarRep
#> 2         0     0.0000
#> 3         0     0.0004
#> 4         0     0.0004
#> 6         0     0.0004
#> 7         0     0.0005
#> 9         0     0.0004
#> 
#> Correlation Matrices 
#> 
#> $one1
#>          ASSSCI  ASMMAT   books migrant
#> ASSSCI   1.0000  0.8292  0.3739 -0.3402
#> ASMMAT   0.8292  1.0000  0.3379 -0.2287
#> books    0.3739  0.3379  1.0000 -0.2537
#> migrant -0.3402 -0.2287 -0.2537  1.0000
#> 
res1$parnames
#>  [1] "ASSSCI_ASSSCI"   "ASSSCI_ASMMAT"   "ASSSCI_books"    "ASSSCI_migrant" 
#>  [5] "ASMMAT_ASMMAT"   "ASMMAT_books"    "ASMMAT_migrant"  "books_books"    
#>  [9] "books_migrant"   "migrant_migrant"
  ##    [1] "ASSSCI_ASSSCI"   "ASSSCI_ASMMAT"   "ASSSCI_books"    "ASSSCI_migrant"
  ##    [5] "ASMMAT_ASMMAT"   "ASMMAT_books"    "ASMMAT_migrant"  "books_books"
  ##    [9] "books_migrant"   "migrant_migrant"

# define four derived parameters
derived.parameters <- list(
        # squared correlation of science and mathematics
        "R2_sci_mat"=~ I( 100* ASSSCI_ASMMAT^2  ),
        # partial correlation of science and mathematics controlling for books
        "parcorr_sci_mat"=~ I( ( ASSSCI_ASMMAT - ASSSCI_books * ASMMAT_books ) /
                            sqrt(( 1 - ASSSCI_books^2 ) * ( 1-ASMMAT_books^2 ) ) ),
        # original correlation science and mathematics (already contained in res1)
        "cor_sci_mat"=~ I(ASSSCI_ASMMAT),
        # original correlation books and migrant
        "cor_book_migra"=~ I(books_migrant)
        )

# statistical inference for derived parameters
res2 <- BIFIEsurvey::BIFIE.derivedParameters( res1, derived.parameters )
summary(res2)
#> ------------------------------------------------------------
#> BIFIEsurvey 3.8.0 () 
#> 
#> Function 'BIFIE.derivedParameters'
#> 
#> Call:
#> BIFIEsurvey::BIFIE.derivedParameters(BIFIE.method = res1, derived.parameters = derived.parameters)
#> 
#> Date of Analysis: 2026-01-11 08:35:24.997193 
#> Time difference of 0.07594967 secs
#> Computation time: 0.07594967 
#> 
#> Multiply imputed dataset
#> 
#> Number of persons = 4668 
#> Number of imputed datasets = 5 
#> Number of Jackknife zones per dataset = 75 
#> Fay factor = 1 
#> 
#> Formulas for Derived Parameters 
#> 
#> R2_sci_mat := I(100 * ASSSCI_ASMMAT^2) 
#> parcorr_sci_mat := I((ASSSCI_ASMMAT - ASSSCI_books * ASMMAT_books)/sqrt((1 - ASSSCI_books^2) * (1 - ASMMAT_books^2))) 
#> cor_sci_mat := I(ASSSCI_ASMMAT) 
#> cor_book_migra := I(books_migrant) 
#> 
#> Statistical Inference for Derived Parameters 
#> 
#>         parmlabel    coef     se        t    df p    fmi  VarMI VarRep
#> 1      R2_sci_mat 68.7673 1.4845  46.3232 13.45 0 0.5453 1.0014 1.0021
#> 2 parcorr_sci_mat  0.8053 0.0092  87.8583 14.40 0 0.5270 0.0000 0.0000
#> 3     cor_sci_mat  0.8292 0.0090  92.6156 13.43 0 0.5457 0.0000 0.0000
#> 4  cor_book_migra -0.2537 0.0209 -12.1266   Inf 0 0.0445 0.0000 0.0004
#> 
#> D1 and D2 Statistic for Wald Test 
#> 
#>         D1     D2 df1 D1_df2 D2_df2 D1_p   D2_p
#> 1 22085063 9.7456   4   38.5    1.7    0 0.1179