Resampling variances for svy2lme

Description

Computes variance estimates for the weighted-pairwise-likelihood linear mixed models fitted by svy2lme using replicate weights. The replicate weights for a pair are obtained by dividing by the sampling weight and then multiplying by the replicate weight. There will be a warning if the ratio of replicate weight to sampling weight differs for observations in the same pair.

Usage

boot2lme(model, rdesign,  verbose = FALSE)
## S3 method for class 'boot2lme'
vcov(object,
   parameter=c("beta", "theta","s2", "relSD" ,"SD","relVar","fullVar"),
   ...)

Arguments

Details

The variance is estimated from the replicates thetastar and original point estimate theta as scale*sum(rscales* (thetastar-theta)^2).

Value

For boot2lme, an object of class boot2lme with components

For the vcov method, a variance matrix.

Examples

data(api, package="survey")

# two-stage cluster sample
dclus2<-svydesign(id=~dnum+snum, fpc=~fpc1+fpc2, data=apiclus2)

m0<-svy2lme(api00~(1|dnum)+ell+mobility, design=dclus2,return.devfun=TRUE)
jkdes<-as.svrepdesign(dclus2, type="mrb")
jkvar<-boot2lme(m0,jkdes)

SE(jkvar, "beta")
SE(jkvar, "SD")
SE(jkvar,"s2")


m1<-svy2lme(api00~(1|dnum)+ell+mobility,
design=dclus2,return.devfun=TRUE, all.pairs=TRUE, subtract.margins=TRUE)
jk1var<-boot2lme(m1,jkdes)

SE(jk1var, "beta")
SE(jk1var, "SD")



##takes a few minutes
data(pisa)

pisa$w_condstuwt<-with(pisa, w_fstuwt/wnrschbw)
pisa$id_student<-1:nrow(pisa)

dpisa<-survey::svydesign(id=~id_school+id_student, weight=~wnrschbw+w_condstuwt, data=pisa)

m<-svy2lme(isei~(1+female|id_school)+female+high_school+college+one_for+both_for+test_lang,
	design=dpisa, return.devfun=TRUE,method="nested")

bpisa<-as.svrepdesign(dpisa, type="bootstrap", replicates=100)

b<-boot2lme(m, bpisa, verbose=TRUE)
str(b)

vcov(b,"beta")
vcov(b,"s2")

## SE() inherits the parameter= argument
SE(b,"beta")
SE(b,"theta")
SE(b,"SD")

Milk production (subset)

Description

A subset of a dataset from the pedigreemm package, created as an example for the lme4qtl package. The original data had records of the milk production of 3397 lactations from first through fifty parity Holsteins. These were 1,359 cows, daughters of 38 sires in 57 herds. The data was downloaded from the USDA internet site. All lactation records represent cows with at least 100 days in milk, with an average of 347 days. Milk yield ranged from 4,065 to 19,345 kg estimated for 305 days, averaging 11,636 kg. There were 1,314, 1,006, 640, 334 and 103 records were from first thorough fifth lactation animals. The subset is of cows from 3 sires.

Usage

data("milk_subset")

Format

A data frame with 316 observations on the following 13 variables.

id

numeric identifier of cow

lact

number of lactation for which production is measured

herd

a factor indicating the herd

sire

a factor indicating the sire

dim

number of days in milk for that lactation

milk

milk production estimated at 305 days

fat

fat production estimated at 305 days

prot

protein production estimated at 305 days

scs

the somatic cell score

sdMilk

milk scaled by cow-specific standard deviation

herd_id

a character vector indicating the herd

one

a vector of 1s for convenience in weighting

one2

another vector of 1s for convenience in weighting

Details

This data example gives noticeably different results for full likelihood and pairwise likelihood because the model is misspecified. The best fitting linear model for the large herd 89 is different, and that herd gets relatively more weight in the pairwise analysis (because it has more pairs).

Source

Constructed at https://github.com/variani/lme4qtl/blob/master/vignettes/pedigreemm.Rmd

References

2010. A.I. Vazquez, D.M. Bates, G.J.M. Rosa, D. Gianola and K.A. Weigel. Technical Note: An R package for fitting generalized linear mixed models in animal breeding. Journal of Animal Science, 88:497-504.

Examples

data(milk_subset)
herd_des<- svydesign(id = ~herd + id, prob = ~one + one2, data = milk_subset)
lm(sdMilk ~ lact + log(dim),data=milk_subset,subset=herd==89)
lm(sdMilk ~ lact + log(dim),data=milk_subset,subset=herd!=89)
svy2lme(sdMilk ~ lact + log(dim) + (1|herd), design=herd_des,method="nested")
svy2lme(sdMilk ~ lact + log(dim) + (1|herd), design=herd_des,method="general")

## pairwise result is closer to herd 89 than to remainder
lme4::lmer(sdMilk ~ lact + log(dim) + (1|herd), data=milk_subset)
svy2relmer(sdMilk ~ lact + log(dim) + (1|id) + (1|herd), design=herd_des,
    relmat = list(id = A_gen))

## compare to all pairs
svy2lme(sdMilk ~ lact + log(dim) + (1|herd),
design=herd_des,method="general", all.pairs=TRUE)
svy2lme(sdMilk ~ lact + log(dim) + (1|herd),
design=herd_des,method="general", all.pairs=TRUE, subtract.margins=TRUE)

Maths Performance Data from the PISA 2012 survey in New Zealand

Description

Data on maths performance, gender, some problem-solving variables and some school resource variables.

Usage

data("nzmaths")

Format

A data frame with 4291 observations on the following 26 variables.

SCHOOLID

School ID

CNT

Country id: a factor with levels New Zealand

STRATUM

a factor with levels NZL0101 NZL0102 NZL0202 NZL0203

OECD

Is the country in the OECD?

STIDSTD

Student ID

ST04Q01

Gender: a factor with levels Female Male

ST14Q02

Mother has university qualifications No Yes

ST18Q02

Father has university qualifications No Yes

MATHEFF

Mathematics Self-Efficacy: numeric vector

OPENPS

Mathematics Self-Efficacy: numeric vector

PV1MATH,PV2MATH,PV3MATH,PV4MATH,PV5MATH

'Plausible values' (multiple imputations) for maths performance

W_FSTUWT

Design weight for student

SC35Q02

Proportion of maths teachers with professional development in maths in past year

PCGIRLS

Proportion of girls at the school

PROPMA5A

Proportion of maths teachers with ISCED 5A (math major)

ABGMATH

Does the school group maths students: a factor with levels No ability grouping between any classes One of these forms of ability grouping between classes for s One of these forms of ability grouping for all classes

SMRATIO

Number of students per maths teacher

W_FSCHWT

Design weight for school

condwt

Design weight for student given school

Source

A subset extracted from the PISA2012lite R package, https://github.com/pbiecek/PISA2012lite

References

OECD (2013) PISA 2012 Assessment and Analytical Framework: Mathematics, Reading, Science, Problem Solving and Financial Literacy. OECD Publishing.

Examples

data(nzmaths)

oo<-options(survey.lonely.psu="average") ## only one PSU in one of the strata

des<-svydesign(id=~SCHOOLID+STIDSTD, strata=~STRATUM, nest=TRUE,
	weights=~W_FSCHWT+condwt, data=nzmaths)

## This example works, but it takes more than five seconds to run, so it
## has been commented out
## m1<-svy2lme(PV1MATH~ (1+ ST04Q01 |SCHOOLID)+ST04Q01*(PCGIRLS+SMRATIO)+MATHEFF+OPENPS, design=des)

options(oo)

Data from the PISA international school survey

Description

Data from the PISA survey of schools, obtained from Stata, who obtained it from Rabe-Hesketh & Skrondal.

Usage

data("pisa")

Format

A data frame with 2069 observations on the following 11 variables.

female

1 for female

isei

socioeconomic index

w_fstuwt

student sampling weight (total)

wnrschbw

school sampling weight

high_school

1 if highest level of parents' education is high school

college

1 if highest level of parents' education is college/uni

one_for

1 if one parent is foreign-born

both_for

1 if both parents are foreign-born

test_lang

1 if the test language is spoken at home

pass_read

1 if the student passed a reading proficiency test

id_school

school (sampling unit) identifier

Source

Data downloaded from https://www.stata-press.com/data/r15/pisa2000.dta

References

Rabe-Hesketh, S., and A. Skrondal. 2006. Multilevel modelling of complex survey data.Journal of the Royal Statistical Society, Series A. 169: 805-827

Examples

data(pisa)

## This model doesn't make a lot of sense, but it's the one in the
## Stata documentation because the outcome variable is numeric.

pisa$w_condstuwt<-with(pisa, w_fstuwt/wnrschbw)
pisa$id_student<-1:nrow(pisa)

dpisa<-survey::svydesign(id=~id_school+id_student, weight=~wnrschbw+w_condstuwt, data=pisa)


svy2lme(isei~(1|id_school)+female+high_school+college+one_for+both_for+test_lang,
	design=dpisa)

Linear mixed models by pairwise likelihood

Description

Fits linear mixed models to survey data by maximimising the profile pairwise composite likelihood.

Usage

svy2lme(formula, design, sterr=TRUE,  return.devfun=FALSE,
method=c("general","nested"), all.pairs=FALSE, subtract.margins=FALSE)
## S3 method for class 'svy2lme'
coef(object,...,random=FALSE)

Arguments

Details

The population pairwise likelihood would be the sum of the loglikelihoods for a pair of observations, taken over all pairs of observations from the same cluster. This is estimated by taking a weighted sum over pairs in the sample, with the weights being the reciprocals of pairwise sampling probabilities. The advantage over standard weighted pseudolikelihoods is that there is no large-cluster assumption needed and no rescaling of weights. The disadvantage is some loss of efficiency and simpler point estimation.

With method="nested" we have the method of Yi et al (2016). Using method="general" relaxes the conditions on the design and model.

The code uses lme4::lmer to parse the formula and produce starting values, profiles out the fixed effects and residual variance, and then uses minqa::bobyqa to maximise the resulting profile deviance.

As with lme4::lmer, the default is to estimate the correlations of the random effects, since there is typically no reason to assume these are zero. You can force two random effects to be independent by entering them in separate terms, eg (1|g)+(-1+x|g) in the model formula asks for a random intercept and a random slope with no random intercept, which will be uncorrelated.

The internal parametrisation of the variance components uses the Cholesky decomposition of the relative variance matrix (the variance matrix divided by the residual variance), as in lme4::lmer. The component object$s2 contains the estimated residual variance and the component object$opt$par contains the elements of the Cholesky factor in column-major order, omitting any elements that are forced to be zero by requiring indepedent random effects.

Standard errors of the fixed effects are currently estimated using a "with replacement" approximation, valid when the sampling fraction is small and superpopulation (model, process) inference is intended. Tthe influence functions are added up within cluster, centered within strata, the residuals added up within strata, and then the crossproduct is taken within each stratum. The stratum variance is scaled by ni/(ni-1) where ni is the number of PSUs in the stratum, and then added up across strata. When the sampling and model structure are the same, this is the estimator of Yi et al, but it also allows for there to be sampling stages before the stages that are modelled, and for the model and sampling structures to be different.

The return.devfun=TRUE option is useful if you want to examine objects that aren't returned as part of the output. For example, get("ij", environment(object$devfun)) is the set of pairs used in computation.

Value

svy2lme returns an object with print, coef, and vcov methods.

The coef method with random=TRUE returns a two-element list: the first element is the estimated residual variance, the second is the matrix of estimated variances and covariances of the random effects.

Author(s)

Thomas Lumley

References

J.N.K. Rao, François Verret and Mike A. Hidiroglou "A weighted composite likelihood approach to inference for two-level models from survey data" Survey Methodology, December 2013 Vol. 39, No. 2, pp. 263-282

Grace Y. Yi , J. N. K. Rao and Haocheng Li "A WEIGHTED COMPOSITE LIKELIHOOD APPROACH FOR ANALYSIS OF SURVEY DATA UNDER TWO-LEVEL MODELS" Statistica Sinica Vol. 26, No. 2 (April 2016), pp. 569-587

Examples

data(api, package="survey")

# one-stage cluster sample
dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)
# two-stage cluster sample
dclus2<-svydesign(id=~dnum+snum, fpc=~fpc1+fpc2, data=apiclus2)

svy2lme(api00~(1|dnum)+ell+mobility+api99, design=dclus1)
svy2lme(api00~(1|dnum)+ell+mobility+api99, design=dclus2)
svy2lme(api00~(1|dnum)+ell+mobility+api99, design=dclus2,method="nested")

lme4::lmer(api00~(1|dnum)+ell+mobility+api99, data=apipop)

## Simulated

set.seed(2000-2-29)

df<-data.frame(x=rnorm(1000*20),g=rep(1:1000,each=20), t=rep(1:20,1000), id=1:20000)
df$u<-with(df, rnorm(1000)[g])

df$y<-with(df, x+u+rnorm(1000,s=2))

## oversample extreme `u` to bias random-intercept variance
pg<-exp(abs(df$u/2)-2.2)[df$t==1]

in1<-rbinom(1000,1,pg)==1
in2<-rep(1:5, length(in1))

sdf<-subset(df, (g %in% (1:1000)[in1]) & (t %in% in2))

p1<-rep(pg[in1],each=5)
N2<-rep(20,nrow(sdf))

## Population values
lme4::lmer(y~x+(1|g), data=df)

## Naive estimator: higher intercept variance
lme4::lmer(y~x+(1|g), data=sdf)

##pairwise estimator
sdf$w1<-1/p1
sdf$w2<-20/5

design<-survey::svydesign(id=~g+id, data=sdf, weights=~w1+w2)
pair<-svy2lme(y~x+(1|g),design=design,method="nested")
pair

pair_g<-svy2lme(y~x+(1|g),design=design,method="general")
pair_g

all.equal(coef(pair), coef(pair_g))
all.equal(SE(pair), SE(pair_g))

Linear mixed models with correlated random effects

Description

Fits linear mixed models by maximising the profile pairwise composite likelihood. Allows for correlated random effects, eg, for genetic relatedness (QTL) models

Usage

svy2relmer(formula, design, sterr=TRUE, return.devfun=FALSE, relmat=NULL,
 all.pairs=FALSE, subtract.margins=FALSE )

Arguments

Details

This function is very similar to svy2lme and only the differences are described here.

Formula parsing and starting values use code based on the lme4qtl package.

In svy2lme and lme4::lmer, the model is based on independent standard Normal random effects that are transformed to give random coefficients that might be correlated within observation but are either identical or independent between observations. In this function, the basic random effects in a term are multiplied by a square root of the relmat matrix for that term, giving basic random effects whose covariance between observations proportional to the relmat matrix. For example, in a quantitative trait locus model in genetics, the matrix would be a genetic relatedness matrix.

The relmat matrices must have dimnames for matching to the id variable. It is permissible for the relmat matrices to be larger than necessary – eg, containing related units that are not in the sample – since the dimnames will be used to select the relevant submatrix.

There can be only one random-effect term for each relmat term. If you need more, make a copy of the term with a different name.

The return.devfun=TRUE option is useful if you want to examine objects that aren't returned as part of the output. For example, get("ij", environment(object$devfun)) is the set of pairs used in computation.

Value

svy2relmer returns an object with print, coef, and vcov methods.

Author(s)

Thomas Lumley

References

Ziyatdinov, A., Vázquez-Santiago, M., Brunel, H. et al. lme4qtl: linear mixed models with flexible covariance structure for genetic studies of related individuals. BMC Bioinformatics 19, 68 (2018). https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-018-2057-x

Examples

data(milk_subset)
herd_des<- svydesign(id = ~herd + id, prob = ~one + one2, data = milk_subset)

svy2lme(sdMilk ~ lact + log(dim) + (1|herd), design=herd_des, method="general")

svy2relmer(sdMilk ~ lact + log(dim) + (1|id) + (1|herd), design=herd_des,
    relmat = list(id = A_gen))