1 A new version of the CALMAR calibration adjustment program.

1

A new version of the A new version of the

CALMAR CALMAR

calibration adjustment calibration adjustment

programprogram

2

The CALMAR2 The CALMAR2 macros macros

3

I.1. Background

CALMAR = CALibration on MARgins

CALMAR 1 = SAS macro program, written in 1992-1993 at

France’s INSEE by Sautory

Scope : implementing calibration methods developped by

Deville & Särndal (JASA, 1992)

CALMAR 2 = SAS macro, written in 2000 at France’s INSEE

Scope : implementing generalized calibration method for

handling total non-response (Deville, 1998)

4

I.2. What’s new in CALMAR 2

• Simultaneous calibration with 2 or 3 levels

• Total non- response adjustment using generalized calibration

• Handling collinearities between auxiliary variables

• A 5th distance function : generalized hyperbolic sine

• Interactive screens to enter parameters, thanks to

CALMAR2_GUIDE

5

SimultaneousSimultaneous ccalibrationalibration

6

Informations are collected at several levels of observation :

• households + every household’s member

or : firms + every establishment of the firms

i.e. cluster sampling survey, including questions about the clusters

• households + some of their members (Kish individuals)

i.e. two-stages sampling, including questions about the primary units (P.U.)

• households + every household’s member + Kish units

+ auxiliary information available at every level

II.1. The method

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How performing calibration ?

• Independent calibration at every level of observation

• Simultaneous calibration (or "integrated") :

- same weights for all members of a household

- consistency between statistics obtained from varied data files

Simultaneous calibration method

A single calibration is performed at the P.U. level, after having computed the calibration variables totals defined at the secondary levels for each P.U. (Sautory, 1996)

8

II.2. An example

• households (sM sample)

• all the members of the selected households (sI sample)

• one member (Kish individual) in each selected household m, chosen by simple random sampling among

the eligible members of the household (sK sample)

Weight of the household m :

Weight of the member i of the household m :

Weight of the Kish-individual of the household m :

mm 1/πd

mmim, housidd

mk

me

mmk eddm

9

= auxiliary variables vector for each household m in

= vector of the known auxiliary variables totals in the households population

= auxiliary variables vector for each individual (m,i) in sI

= vector of the known totals in the individuals population

= auxiliary variables vector for the Kish- individual in

= vector of the known totals in the Kish-units population

mx

mUm

mxX

MU

im,z

IU

Ms

IUi

izZ

mk

Ksmkv

eIUi

ivV

Auxiliary information

eIU

10

For each household m we compute :

• the totals of the individual variables :

• the estimated totals of the Kish- individual variables :

Vector of the calibration variables for the household m :

Vector of the totals : (X , Z, V)

Calibration equations :

mmeni)(m,

im,m zz

)v,z,(x mmm

mkmm vev

Msm

mmmmmmm V),Z,(X)v,z,(xγ)vμzλxF(d

11

weights

= weight of the household m in

= weight of the individual (m,i) of the

household m in

= weight of the Kish-individual of the

household m in

The 3 samples are correctly calibrated on totals X, Z et V :

mw

Ms

mim, ww

Is

mmk ewwm mk

Ks

Km Km

m

Km

mm

skm

skmk

skmmkk Vvwvewvw

mw

I MM msi smmm

sm meniim,mim,im, Zzwzwzw

12

The user must provide the entry tables for the various

levels (sample data files and calibration variables totals

files) : the program performs all the required operations

necessary to reduce the process to a single calibration,

and creates the varied calibrated weights files.

Calmar 2 performs such simultaneous calibrations.

13

An example of An example of simultaneoussimultaneous

ccalibrationalibration

14

The survey• Sampling design : two stages sampling

– primary units = households, selected by stratified sampling with S.R.S. in the stratum

– secondary units (Kish-units) = one member per selected household, withdrawn by S.R.S. among more than 14 years old members

• Questionary– variables of interest are measured on Kish-units – questions about the habitation and the whole family– questions about each member of the household (age, sex, profession)

• Calibration variables (xk)– Households : household size + head of household professional group

+ strata (~ agglomeration size) – All individuals : sex + age group– Kish individuals : sex + age group

• Population totals (X) come from the sampling frame

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The program

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• %CALMAR2 (datamen=base.echant_menages,• marmen=base.marge_men,• poids=poids1,• ident=ident,• dataind=base.echant_indiv,• marind=base.marge_ind,• ident2=id,• datakish=base.echant_kish,• markish=base.marge_kish,• poidkish=nbelig,• m=1,• datapoi=poidsmen,• datapoi2=poidsind,• datapoi3=poidskish,• poidsfin=w3,• labelpoi=calage 3 niveaux, • poidskishfin=w3k,• labelpoikish=poids kish total,• edition=3)

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The output

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**********************************

*** PARAMÈTRES DE LA MACRO *** **********************************

TABLE(S) EN ENTRÉE : TABLE DE DONNÉES DE NIVEAU 1 DATAMEN = BASE.ECHANT_MENAGES IDENTIFIANT DU NIVEAU 1 IDENT = IDENT TABLE DE DONNÉES DE NIVEAU 2 DATAIND = BASE.ECHANT_INDIV IDENTIFIANT DU NIVEAU 2 IDENT2 = ID TABLE DES INDIVIDUS KISH DATAKISH = BASE.ECHANT_KISH PONDÉRATION INITIALE POIDS = POIDS1 FACTEUR D'ÉCHELLE ECHELLE = 1 PONDÉRATION QK PONDQK = __UN PONDÉRATION KISH POIDKISH = NBELIG

TABLE(S) DES MARGES : DE NIVEAU 1 MARMEN = BASE.MARGE_MEN DE NIVEAU 2 MARIND = BASE.MARGE_IND DE NIVEAU KISH MARKISH = BASE.MARGE_KISH MARGES EN POURCENTAGES PCT = NON EFFECTIF DANS LA POPULATION : DES ÉLÉMENTS DE NIVEAU 1 POPMEN = DES ÉLÉMENTS DE NIVEAU 2 POPIND = DES ÉLÉMENTS KISH POPKISH =

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MÉTHODE UTILISÉE M = 1 BORNE INFÉRIEURE LO = BORNE SUPÉRIEURE UP = COEFFICIENT DU SINUS HYPERBOLIQUE ALPHA = 1 SEUIL D'ARRÊT SEUIL = 0.0001 NOMBRE MAXIMUM D'ITÉRATIONS MAXITER = 15 TRAITEMENT DES COLINÉARITÉS COLIN = NON

TABLE(S) CONTENANT LA POND. FINALE DE NIVEAU 1 DATAPOI = POIDSMEN DE NIVEAU 2 DATAPOI2 = POIDSIND DE NIVEAU KISH DATAPOI3 = POIDSKISH MISE À JOUR DE(S) TABLE(S) DATAPOI(2)(3) MISAJOUR = OUI PONDÉRATION FINALE POIDSFIN = W3 LABEL DE LA PONDÉRATION FINALE LABELPOI = CALAGE 3

NIVEAUX PONDÉRATION FINALE DES UNITES KISH POIDSKISHFIN = W3K LABEL DE LA PONDÉRATION KISH LABELPOIKISH = POIDS KISH

TOTAL CONTENU DE(S) TABLE(S) DATAPOI(2)(3) CONTPOI = OUI

ÉDITION DES RÉSULTATS EDITION = 3 ÉDITION DES POIDS EDITPOI = NON STATISTIQUES SUR LES POIDS STAT = OUI CONTRÔLES CONT = OUI TABLE CONTENANT LES OBS. ÉLIMINÉES OBSELI = NON NOTES SAS NOTES = NON

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COMPARAISON ENTRE LES MARGES TIRÉES DE L'ÉCHANTILLON (PONDÉRATION INITIALE) ET LES MARGES DANS LA POPULATION (MARGES DU CALAGE)

MARGE MARGE POURCENTAGE POURCENTAGE VARIABLE MODALITÉ ÉCHANTILLON POPULATION ÉCHANTILLON POPULATION

NBIND 01 1525.60 1539 26.30 26.53 02 1914.37 1860 33.00 32.06 03 797.71 1000 13.75 17.24 04 930.78 885 16.05 15.26 05 365.18 361 6.30 6.22 06 267.36 156 4.61 2.69

PCSPR 1 80.70 124 1.39 2.14 2 191.78 290 3.31 5.00 3 822.81 624 14.18 10.76 4 832.34 870 14.35 15.00 5 569.41 682 9.82 11.76 6 1279.53 1237 22.06 21.32 7 1839.32 1831 31.71 31.56 8 185.11 143 3.19 2.47

STRATE 0 1453.00 1453 25.05 25.05 1 966.00 966 16.65 16.65 2 805.00 805 13.88 13.88 3 1689.00 1689 29.12 29.12 4 888.00 888 15.31 15.31

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AGE 00-14 ans 3245.32 2857 21.46 19.52

15-24 ans 2217.86 2044 14.67 13.96

25-59 ans 6699.70 6800 44.31 46.45

60- ? ans 2957.50 2939 19.56 20.08

SEXE 1 7546.69 7108 49.91 48.55

2 7573.69 7532 50.09 51.45

AGEK A15 2155.94 2044 18.28 17.35

A25 6752.61 6800 57.25 57.71

A60 2885.84 2939 24.47 24.94

SEXEK 1 5596.30 5673 47.45 48.15

2 6198.09 6110 52.55 51.85

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MÉTHODE : LINÉAIRE

PREMIER TABLEAU RÉCAPITULATIF DE L'ALGORITHME

LA VALEUR DU CRITÈRE D'ARRÊT ET LE NOMBRE DE POIDS NÉGATIFS APRÈS CHAQUE ITÉRATION

CRITÈRE POIDS

ITÉRATION D'ARRÊT NÉGATIFS

1 1.31960 1

2 0.00000 1

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MÉTHODE : LINÉAIREDEUXIÈME TABLEAU RÉCAPITULATIF DE L'ALGORITHME

LES COEFFICIENTS DU VECTEUR LAMBDA DE MULTIPLICATEURS DE LAGRANGE APRÈS CHAQUE ITÉRATION

VARIABLE MODALITÉ LAMBDA1 LAMBDA2

NBIND 01 -0.15325 -0.15325 NBIND 02 -0.24295 -0.24295

NBIND 03 0.00562 0.00562

NBIND 04 -0.17355 -0.17355

NBIND 05 -0.00502 -0.00502

NBIND 06 -0.44773 -0.44773

PCSPR 1 0.92036 0.92036

PCSPR 2 0.50376 0.50376

PCSPR 3 -0.18514 -0.18514

PCSPR 4 0.15354 0.15354

PCSPR 5 0.36019 0.36019

PCSPR 6 0.08424 0.08424

PCSPR 7 0.16042 0.16042

PCSPR 8 . .

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VARIABLE MODALITÉ LAMBDA1 LAMBDA2

STRATE 0 -0.14172 -0.14172 STRATE 1 -0.07338 -0.07338 STRATE 2 -0.12634 -0.12634 STRATE 3 -0.03106 -0.03106

STRATE 4 . . AGE 00-14 ans -0.03549 -0.03549 AGE 15-24 ans -0.65576 -0.65576 AGE 25-59 ans -0.52872 -0.52872 AGE 60- ? ans -0.64430 -0.64430 SEXE 1 -0.08395 -0.08395

SEXE 2 . . AGEK A15 0.67198 0.67198 AGEK A25 0.68366 0.68366 AGEK A60 0.74262 0.74262 SEXEK 1 0.01727 0.01727

• SEXEK 2 . .

25


NBIND 01 1539 1539 26.53 26.53 02 1860 1860 32.06 32.06 03 1000 1000 17.24 17.24 04 885 885 15.26 15.26 05 361 361 6.22 6.22 06 156 156 2.69 2.69

PCSPR 1 124 124 2.14 2.14 2 290 290 5.00 5.00 3 624 624 10.76 10.76 4 870 870 15.00 15.00 5 682 682 11.76 11.76 6 1237 1237 21.32 21.32 7 1831 1831 31.56 31.56 8 143 143 2.47 2.47 STRATE 0 1453 1453 25.05 25.05 1 966 966 16.65 16.65 2 805 805 13.88 13.88 3 1689 1689 29.12 29.12 4 888 888 15.31 15.31

COMPARAISON ENTRE LES MARGES FINALES DANS L'ÉCHANTILLON (AVEC LA PONDÉRATION FINALE)

ET LES MARGES DANS LA POPULATION (MARGES DU CALAGE)

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MARGE MARGE POURCENTAGE POURCENTAGE

VARIABLE MODALITÉ ÉCHANTILLON POPULATION ÉCHANTILLON POPULATION

AGE 00-14 ans 2857 2857 19.52 19.52 15-24 ans 2044 2044 13.96 13.96 25-59 ans 6800 6800 46.45 46.45 60- ? ans 2939 2939 20.08 20.08

SEXE 1 7108 7108 48.55 48.55 2 7532 7532 51.45 51.45

AGEK A15 2044 2044 17.35 17.35 A25 6800 6800 57.71 57.71 A60 2939 2939 24.94 24.94

SEXEK 1 5673 5673 48.15 48.15 2 6110 6110 51.85 51.85

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STATISTIQUES SUR LES RAPPORTS DE POIDS(= PONDÉRATIONS FINALES / PONDÉRATIONS INITIALES)

ET SUR LES PONDÉRATIONS FINALES

The UNIVARIATE Procedure Variable: _F_ (RAPPORT DE POIDS)

Basic Statistical Measures

Quantiles (Definition 5) Location Variability Quantile Estimate

Mean 1.000000 Std Deviation 0.24564 100% Max 2.009262 Median 0.996533 Variance 0.06034 99% 1.745002 Mode 0.991339 Range 2.32886 95% 1.377982 Interquartile Range 0.21258 90% 1.278637 75% Q3 1.105492 50% Median 0.996533 25% Q1 0.892917 10% 0.749877 5% 0.613091 1% 0.251528 0% Min -0.319601 Extreme Observations

-------------Lowest------------- ------------Highest-----------

Value IDENT Obs Value IDENT Obs

-0.3196012 1163032100 27 1.76397 5363019600 293 0.0374385 7363016270 365 1.79618 7463000450 381 0.1498661 1169040310 73 1.85813 2369004180 129 0.1872096 7269001420 348 1.97094 5463007950 326 0.2314417 7363017990 366 2.00926 5263016110 268

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STATISTIQUES SUR LES RAPPORTS DE POIDS (= PONDÉRATIONS FINALES / PONDÉRATIONS INITIALES)


The UNIVARIATE Procedure

Variable: _F_ (RAPPORT DE POIDS)

Histogram # Boxplot 2.05+* 1 * .* 1 * .* 1 * .* 3 0 .* 3 0 .** 5 0 .*** 7 0 .********* 26 | .********* 27 | .******************** 59 +-----+ .************************************* 110 | + | .******************************************* 128 *-----* 0.85+******************* 57 +-----+ .*********** 33 | .****** 17 | .*** 8 0 .** 5 0 .* 3 0 .* 2 0 .* 2 * .* 1 * . . . -0.35+* 1 * ----+----+----+----+----+----+----+----+--- * may represent up to 3 counts

29

STATISTIQUES SUR LES RAPPORTS DE POIDS (= PONDÉRATIONS FINALES / PONDÉRATIONS INITIALES)ET SUR LES PONDÉRATIONS FINALES

The UNIVARIATE Procedure Variable: __WFIN (PONDÉRATION FINALE)

Basic Statistical Measures

Quantiles (Definition 5) Location Variability Quantile Estimate

Mean 11.60200 Std Deviation 4.62597 100% Max 29.19457 Median 10.11949 Variance 21.39957 99% 25.69548 Mode 9.57633 Range 32.03263 95% 20.11085 Interquartile Range 5.70090 90% 18.04434

75% Q3 13.98763 50% Median 10.11949 25% Q1 8.28672 10% 7.15056 5% 6.41373 1% 2.50660 0% Min -2.83806 Extreme Observations

-------------Lowest------------ ------------Highest-----------

Value IDENT Obs Value IDENT Obs

-2.838058 1163032100 27 25.7604 5369016540 317 0.543982 7363016270 365 26.0985 7463000450 381 1.330811 1169040310 73 28.6378 5463007950 326 1.808444 7269001420 348 28.6643 8269018030 421 2.235727 7363017990 366 29.1946 5263016110 268

30

STATISTIQUES SUR LES RAPPORTS DE POIDS (= PONDÉRATIONS FINALES / PONDÉRATIONS INITIALES)


The UNIVARIATE Procedure

Variable: __WFIN (PONDÉRATION FINALE)

Histogram # Boxplot 29+* 3 0 .* 1 0 .** 4 0 .*** 8 0 .**** 11 | .********* 25 | .************** 41 | .*********** 32 | 13+*********************** 67 +-----+ .********************** 64 *--+--* .********************************************* 134 +-----+ .****************************** 88 | .***** 14 | .** 4 | .* 3 | . -3+* 1 0 ----+----+----+----+----+----+----+----+----+ * may represent up to 3 counts

31

MÉTHODE : LINÉAIRE RAPPORTS DE POIDS MOYENS (PONDÉRATIONS FINALES / PONDÉRATIONS INITIALES)

POUR CHAQUE VALEUR DES VARIABLES

NOMBRE D'OBSERVATIONS RAPPORT VARIABLE MODALITE DE NIVEAU 1 DE POIDS

NBIND 01 133 1.00152 NBIND 02 167 0.97304 NBIND 03 69 1.24647 NBIND 04 79 0.95151 NBIND 05 31 0.99271 NBIND 06 21 0.58818 PCSPR 1 6 1.55064 PCSPR 2 15 1.52001 PCSPR 3 73 0.76645 PCSPR 4 73 1.04281 PCSPR 5 51 1.20566 PCSPR 6 111 0.96902 PCSPR 7 157 0.99429 PCSPR 8 14 0.76191 STRATE 0 100 1.00000 STRATE 1 100 1.00000 STRATE 2 100 1.00000 STRATE 3 100 1.00000 STRATE 4 100 1.00000 ENSEMBLE 500 1.00000

32

MÉTHODE : LINÉAIRE RAPPORTS DE POIDS MOYENS (PONDÉRATIONS FINALES / PONDÉRATIONS INITIALES)

POUR CHAQUE VALEUR DES VARIABLES

NOMBRE D'OBSERVATIONS RAPPORT VARIABLE MODALITE DE NIVEAU 2 DE POIDS

AGE 00-14 an 274 0.88664 AGE 15-24 an 184 0.93210 AGE 25-59 an 581 1.01758 AGE 60- ? an 249 0.99088 SEXE 1 640 0.94443 SEXE 2 648 0.99993 ENSEMBLE 1288 0.97235

NOMBRE D'INDIVIDUS RAPPORT VARIABLE MODALITE KISH DE POIDS

AGEK A15 66 0.95043 AGEK A25 283 1.01108 AGEK A60 151 1.00090 SEXEK 1 232 0.98540 SEXEK 2 268 1.01264 ENSEMBLE 500 1.00000

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MÉTHODE : LINÉAIRE

CONTENU DE LA TABLE poidsmen CONTENANT LA NOUVELLE PONDÉRATION w3

The CONTENTS Procedure

# Variable Type Len Pos Label 1 IDENT Char 10 8 2 w3 Num 8 0 calage 3 niveaux

CONTENU DE LA TABLE poidsind CONTENANT LA NOUVELLE PONDÉRATION w3 # Variable Type Len Pos Label 2 IDENT Char 10 20 1 id Char 12 8 3 w3 Num 8 0 calage 3 niveaux

CONTENU DE LA TABLE poidskish CONTENANT LA NOUVELLE PONDÉRATION w3

# Variable Type Len Pos Label 2 ID Char 12 26 1 IDENT Char 10 16 3 w3 Num 8 0 calage 3 niveaux 4 w3k Num 8 8 poids kish total

34

********************* *** BILAN *** *********************

* * DATE : 24 AOUT 2005 HEURE : 11:12 * * ************************************* * TABLE EN ENTRÉE : BASE.ECHANT_MENAGES * ************************************* * * NOMBRE D'OBSERVATIONS DANS LA TABLE EN ENTRÉE : 500 * NOMBRE D'OBSERVATIONS ÉLIMINÉES : 0 * NOMBRE D'OBSERVATIONS CONSERVÉES : 500 * * VARIABLE DE PONDÉRATION : POIDS1 * * NOMBRE DE VARIABLES CATÉGORIELLES : 3 * LISTE DES VARIABLES CATÉGORIELLES ET DE LEURS NOMBRES DE MODALITÉS : nbind (6) pcspr (8) strate (5) * * SOMME DES POIDS INITIAUX : 5801 * TAILLE DE LA POPULATION : 5801 * * * *********************************** * TABLE EN ENTRÉE : BASE.ECHANT_INDIV * *********************************** * * NOMBRE D'OBSERVATIONS DANS LA TABLE EN ENTRÉE : 1288 * NOMBRE D'OBSERVATIONS ÉLIMINÉES : 0 * NOMBRE D'OBSERVATIONS CONSERVÉES : 1288 * * NOMBRE DE VARIABLES CATÉGORIELLES : 2 * LISTE DES VARIABLES CATÉGORIELLES ET DE LEURS NOMBRES DE MODALITÉS : * age (4) sexe (2)

* SOMME DES POIDS INITIAUX : 15120 * TAILLE DE LA POPULATION : 14640 *

35

* *********************************** * TABLE EN ENTRÉE : BASE.ECHANT_KISH * *********************************** * * NOMBRE D'OBSERVATIONS DANS LA TABLE EN ENTRÉE : 500 * NOMBRE D'OBSERVATIONS ÉLIMINÉES : 0 * NOMBRE D'OBSERVATIONS CONSERVÉES : 500 * * VARIABLE DE PONDÉRATION CONDITIONNELLE : NBELIG * NOMBRE MAXIMUM D'UNITES SECONDAIRES PAR UP : 1 * * NOMBRE DE VARIABLES CATÉGORIELLES : 2 * LISTE DES VARIABLES CATÉGORIELLES ET DE LEURS NOMBRES DE MODALITÉS : agek (3) sexek (2) * * SOMME DES POIDS INITIAUX : 11794 * TAILLE DE LA POPULATION : 11783 * * * MÉTHODE UTILISÉE : LINÉAIRE * LE CALAGE A ÉTÉ RÉALISÉ EN 2 ITÉRATIONS * IL Y A 1 POIDS NÉGATIFS * LES POIDS ONT ÉTÉ STOCKÉS DANS LA VARIABLE W3 DE LA TABLE POIDSMEN * ET DE LA TABLE POIDSIND * ET DE LA TABLE POIDSKISH * LES POIDS DES UNITES KISH ONT ÉTÉ STOCKÉS DANS LA VARIABLE W3K * DE LA TABLE POIDSKISH

36

Handling Handling

total non-response total non-response

with generalized with generalized

calibrationcalibration

37

III.1. Generalized calibration

Calibration functions :

where : vector of p adjustment parameters

Calibration equations :

Solving for

s

kkk XxλzFd

sinablesknown varipofvector:zk

10Fassuch kzF

λzFdw kkk

38

= parameter estimates of the instrumental regression

of on with as instrumental variables,

weighted by

kdkx

skkkk

skkkkszx

szxHTHTireg

kkw

yzdxzdB

BXXYY

ywY

1

s

ˆwhere

ˆˆˆˆ

toequivalentally asymptoticˆ

Basic result

iregwkk YYzzF ˆˆthen,1If

szxB

ky kz

39

Ukkzx

Ukkzxkkk

kkU

kw

yzBxztqBxyE

EdEdΔYAV

Precision

szxkkk

skk

k

kw

Bxye

ededπΔ

YV

= residual of the regression of Y on X in U with the instrumental variables Z

Note : the instruments are equal to

1(0)Fifz

z(0)Fλ)zF(grad

k

k0λk

40

III.2. Calibration in case of total non-response

Calibration after adjustment for non-response

1.a. Adjustment for non-response

Response probabilities (conditionnally to s) :

is estimated referring to a response model and an estimation method

Expansion estimator :

sk/rkPpk

kp kpLM

r

kk

kexp yp1

dY

41

Examples

• Uniform response model :

• Homogeneous response groups :

• Generalized linear model :

vector of explanatory non-response variables

Note : for estimating , must be known both for

respondents AND NON-RESPONDENTS

βzH1

pk

k

hkifn

rp

h

h k

nr

pk

kz

kzkp

42

1.b. Calibration

We start from corrected weights

Conventional calibration :

*k

k

k dpd

r

kk**

k XxμxFd

43

Direct conventional calibration

rkkk XxλxFd

is equivalent to with a uniform non-response model.

Comparison between and (Dupont, 1993)

Let’s suppose :

- N.R. is corrected by a GLM, in which H is one of the usual

calibration functions F :

- non-response variables are included into calibration set of

variables .

Then : and are " similar "

kxkz

kk zF

1p

44

expHFF,zxa *kk

and are identical when :

(b) . N.R. is corrected by HRG model based on a categorical

variable X

. The sample is calibrated on the number of units in U

for

each X level

= = formal post-stratification on U

45

Direct generalized calibration

(E)

Interpretation

Response model :

(E) can be written :

r

kkk XxzHd

0kk zH

1p

λββwith

xλzFp

1d

xβzH

λβzHβzHdx

βzH

βzHβzHdX

0

kr

kk

k

rk

0k

0k0kk

rk

0k

k0kk

46

So, if the were known :

(E) = generalized calibration equation, with :

F is defined as

and such as

0k

0kk zH

zHzF

functionn calibratio F

weightsinitialp

d

k

k

kp

*kk

0k

0k0k zz

zHzH

zFgrad:sinstrument

10F

47

Precision

• uses the residuals in the population

• uses the residuals of the instrumental regression

in r, weighted by the :

estimator for if response probabilities

were known

wYAV

Uxzkk

*k

xzkkk

0Bxyzwhere

BxyE

*

*

wYV

0kk zHd

0xrz*B

xz*B 0k1 zH

rx0rzkk

*k0kk

x0rzkkk

0BxyzβzHdwhere

Bxye

*

*

Response probabilities are unknown

"estimate" and the residuals :

i.e. instrumental regression weighted by final weights

Note : looks like

= estimated variance 1st phase (sample s selection)

= estimated variance 2nd phase (respondents r "selection")

0xrz*B

rxrzkk

*kkk

xrzkkk

0BxyzβzHdwhere

Bxye

*

*

ˆzHdw kkk

wYV

)e(Q)e(QYV k2k1w

1Q

2Q

49

• allows non–response correction even when explanatory variables are only known for respondents

• Handles the particular situation in which non-response explanatory variables are variables of interest (non ignorable response mechanism )

• reduces the bias produced by non–response thanks to variables , and reduces the variance thanks to variables

Properties of the method

kz kx

This method is performed in Calmar 2.

50

An example of An example of generalizedgeneralized c calibrationalibration

51

The survey• Sampling frame : population census (1990)• Sampling design : cluster sampling

– clusters = households– secondary units = all members of selected households

• Response model– H.R.G. – response variables = household size (alone or not) + head of household profession (6 levels) + strata (~ agglomeration size)

• Calibration variables (xk)– Households : the same as before (in the sampling frame)– Individuals : sex + age group (in the sampling frame)– Simultaneous calibration with two levels

• Instrumental variables (zk)– Response variables as they are measured in the survey, that is in 1996

52

The population totals data

Constraint : the xk and zk vectors must have same dimension

• Primary units (households)

var n R mar1 mar2 mar3 mar4 mar5 mar6

strate90 5 0 1314 833 704 1477 777 . seul90 2 0 3933 1172 . . . . cs90 6 0 457 470 537 435 1254 1952 strate96 5 1 . . . . . . seul96 2 1 . . . . . . cs96 6 1 . . . . . .

• Secondary units (individuals)

var n R mar1 mar2 mar3 mar4

sexe 2 0 6255 6628 . . age 4 0 2514 1799 5984 2586 sexe_bis 2 1 . . . . age_bis 4 1 . . . .

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%calmar2_guide

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Merci de votre attention !

1 A new version of the CALMAR calibration adjustment program.

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Transcript of 1 A new version of the CALMAR calibration adjustment program.