a short history of network sampling

8/13/2019 A SHORT HISTORY OF NETWORK SAMPLING

1/6

A S H O R T H I S T O R Y O F N E T W O R K S A M P L IN GMonroe G. S i rken , Na t iona l Cente r for Hea l th S ta t i s t ic s

6525 Be lc res t Road , Room 1000, Hya t t sv i l le , MD. 20782

K e y W o rds : m u l t ip l i c i t y s urv ey ss a m p l i ng h i s t o ry s urv ey des i g nI nt ro duct i o nN e tw o r k s a mp l in g a n d c l a s s i c al s u r v e y s a mp l in g d i f f erw i th r e s p e c t t o t h e c o u n t i n g r u l e p a r a d ig m f o r l i n k in gp o p u la t i o n e l e m e n t s t o t h e s e l e c ti o n u n i t s a t w h ic h t h e ya re countab le in the survey [20]. C lass ica l surveys a m p l i n g u s e s uni t a ry co unt i ng r u l e s , s u c h a s d e j u r eand de f ac to r e s idence ru le s in household surveys , tha ts e e k t o u n iq u e ly l i n k e a c h p e r s o n t o o n e a n d o n lyhousehold . Ne tw ork samp l ing , on the o the r hand , seeksto c a p i t a li z e o n d u p l i c a t e c o u n t i n g o f p o p u l a t io ne l e me n t s b y u s in g m u l t ip l i c i ty co u nt i ng ru le s , such a sf r i e n d s h ip a n d k in s h ip r u l e s in h o u s e h o ld s u r v e y s, t h a tl i n k t h e s a me p e r s o n t o mu l t i p l e h o u s e h o ld s o f t h e irf r iends or r e la t ives .O v e r t h e p a s t t h i r t y y e a r s , n e tw o r k s a mp l in g h a simp r o v e d s u r v e y d e s ig n e f f i c i e n c i e s p a r t i c u l a r l y w h e nc lass ica l sampl ing i s in feas ib le or ine f f ic ien t . D ur in g the1 9 6 0 s , n e tw o r k s a mp l in g w a s a p p l i e d i n e s t a b l is h me n tsurveys when uni ta ry count ing ru le s a re d i f f icu l t tode f ine and execute because the sam e pop ula t ion e lemen tsappea r inext r icab ly l inked to mul t ip le e s tab l i shments .D u r in g t h e 1 9 7 0 s , n e tw o r k s a mp l in g w a s f o s t e re d i nh o u s e h o ld s u r v e y s o f ra r e p o p u l a t io n s i n w h ic h d e j u r eres idence ru le s a re easy enough to de f ine and execute ,bu t the sampl ing e r ror e f fects a re o f ten in to le rab ly la rge .D u r in g t h e 1 9 8 0 s , n e tw o r k s a m p l in g w a s e x t e n d e d t ora re pop ula t ion surveys in which de jure r e s idence ru le sin c u r l a r g e me a s u r e me n t e r r o r s a s w e l l a s s a mp l in ge r ror s . I l l b r ie f ly d iscuss and i l lus t r a te each thesen e tw o r k s a mp l in g a p p l i c a ti o n s .D u r in g t h e 1 9 9 0 s , n e tw o r k s a mp l in g t h e o r y i s b e in ga p p l i e d i n p o p u l a t i o n b a s e d e s t a b l i s h me n t s u r v e y s [ 1 3,23] . In these surveys , e s tab l i shm ents tha t havet r a n s a c t i o n s w i th p e r s o n s e n u me r a t e d i n h o u s e h o lds a mp le s u r v e y s s e r v e a s s a mp l in g f r a me s f o re s t a b l i s h me n t s u r v e ys . P o p u l a t i o n b a s e d e s t a b l is h me n ts ur ve y s p r o v id e a m e c h a n i s m f o r i n t e g r a t i n g t h e s a m p led e s ig n s o f h o u s e h o ld a n d e s t a b l is h me n t s u r v ey s toproduce s ta t i s t ic s about t r ansac t ions tha t people havewi th e s tab l i shme nts . They a re e spec ia l ly appl icab lew h e n f r e e - st a n d in g e s t a b l i s h me n t f r a m e s d o n o t e x i s t o r

i f a v a i la b l e d o n o t h a v e g o o d me a s u r e s o f e s t a b li s h me n tsize.Establ i shment surveys in which uni tary co unt ing rulesare di f f icul t to applyIn the ea r ly 1960 s , r e so lu t ion of an e s t im a t ion problemin a medica l p rovide r survey to e s t ima te the preva lenceof cyst ic f ib ros is [7] u l t ima te ly led to the deve lop me nt o fn e tw o r k s a mp l in g . C l a s s ic a l s a mp l in g e s t ima t io n w a sn o t a p p l i ca b l e i n t h i s s u r v ey b e c a u s e mu l t i p l e m e d ic a lp r o v id e r s o f t e n t r e a t e d a n d h e n c e r e p o r t e d t h e s a mecys t ic f ib ros is pa t ien ts . B i m ba um and S i rken [1]r e s o lv e d t h e p r o b l e m b y p r o p o s in g t h r e e u n b i a s e des t im a tor s for med ica l p rovide r surveys of r a re d iseasep r e v a l e n c e i n w h ic h mu l t i p l e p r o v id e r s a r e e l i g ib l e t orepor t the sam e pa t ien ts .T h e t h r e e e s t ima to r s p r o p o s e d b y B imb a u m a n d S i r k e nut i l ize in forma t ion about the mul t ip l ic i t ie s of medica lprovide r s e l ig ib le to r epor t the same pa t ien ts in thesurvey . Th is in forma t ion a t typ ica l ly co l lec ted when theprovid e r s r epor t the i r pa t ien ts in the survey . Thees t ima tor s d i ff e r f rom each o the r w i th r e spec t to the waythe mul t ip l ic i ty in form a t ion is used . The mult ipl ic i tyes t i m a t o r for example , counts eve ry pa t ien t , a s manyt imes a s he or she i s r epor ted by a d i f f e ren t medica lp r o v id e r i n t h e s a mp le s u r ve y , a n d w e ig h t s e a c h r e p o r tby the inve rse of the pa t ie n t s mu l t ip l ic i ty . On the o the rh a n d , t h e H o r v i t z / T h o m p s o n n e t w o r k es t i m a t o rca lcu la te s the se lec t ion probabi l i t ie s of eve ry pa t ien trepor ted in the survey , and tha t r equi re s count ing then u m b e r o f t ime s t h e s a me p a t i e n t s a r e r e p o r t ed b yd i f f er e n t me d ic a l p r o v id e r s i n t h e s u r ve y , a n d k n o w in gthe m ul t ip l ic i tie s o f eve ry repor ted p a t ien t .S in c e t h e 1 9 6 0 s n e tw o r k s a m p l in g h a s b e e n a p p l i e d i nma n y me d ic a l p r o v id e r s u r v e y s a n d o th e r k in d s o fes tab l ishment surveys . In these appl ica t ions , the des igns t ra teg y i s to se lec t the count ing ru le s tha t min im izeto ta l survey e r ror s [17] . Som et imes , f ie ld exper im entsa r e u n d e r t a k e n t o i n v e s t ig a t e a l t e r n a ti v e c o u n t i n g r u l eoptions.Fo r exam ple , Hend r icks , Sea r le s and Horv i tz [6]compare e f f ic ienc ies of a l te rna t ive count ing ru le s ora s s o c i a ti n g f a r ms a n d c r o p a c r e a g e w i th a r e a l s e g me n t s


2/6

in agriculture sample surveys. Traditionally, agriculturesurveys used the headquarters counting rule. This rulel inks each farm to one and only one area segmentnamely the segment con taining the farm 's headquar ters.Dif f icul t ies in def in ing farm headquar ters , and inimp lem enting th is ru le , led to tes ting the weightedsegm ent ru le . This ru le l inks each farm to every areasegm ent in tersect ing the farm 's boundaries. Farm sintersected by samp le area segments were weighted bythe fractions of the farms' la nd with in the area segments.Th is w e i g h t e d m u l t i p l i c i t y e s t i m a t o r i s an unbiasedes t imat ion procedure, wh en as in th is example the sum sof the f ract ional weights ass igned each farms inintersected area segments equal unity.In Hendr icks ' exper iment , sampling er rors associatedwith the headquar ters were reduced by about 25 to 50percent by area seg me nt rule. Furthermore, interview ersmis interpreted and misappl ied the weighted segmentrule far less frequen tly than th e headqu arters rule.

o u s e h o l d s u r v e y s o f r a r e p o p u l a t io n s a n d e v e n t sNetwork sam pling em erged as a d is t inct type of sampledes ign dur ing the 1970 's when i t was del iberate lyfostered as a design strategy in household surveys of rarepopulat ions that use c o m p o s i t e c o u n t i n g ru les . Theserules have the proper ty of l inking rare persons to theirown residenc es an d to other residences of persons, withwhom they have well defined relationships, such asrelatives, fr iends, o r neighbors.Though composi te count ing rules enumerate morepersons than de jure residence rules, sampling variancesassociated with composi te count ing rules are notnecessar ily smaller [1 4] because other factors arerelevant including the extend of c lus tering, andvar iabi l i ty in the mult ip l ic i t ies [15] . However , whencomposi te count ing rules l ink no more than one rareperson to any household , they reduce var iancesassociated with the de jure ru le by a factor equal to theharmonic mean of the mult ip l ic i t ies of the rarepopulation. If , for exam ple, the composite nile links nomore than one rare person to a household, and assigns allrare persons the same multiplicity, say s , classicalsam pling var iance associated with the de jure ru le isreduced by a factor o f s.On the other hand, reporting biases are often larger forcom posi te c ount ing rules tha n de jure res idence rulesbecause the latter involve collecting supplementarysurvey information. In compliance with both ru les ,households report their residents that have the rare

atm'bute. In addition, in compliance with the co mpositerule, households report the multiplicities of their ownhousehold mem bers having the rare a t tr ibute, an d theyserve as proxy responden ts for non house hold pe rsons towhich they are l inked by the com posi te ru le , and repor twhich of them h ave the rare a t tr ibute , an d theirmultiplicities.Because of the d ifference in the re la t ive magn i tudes ofsampling er rors and repor t ing bias associated w ith thecomposite and de jure counting rules, relative etiicienciesof composite rules typically decrease with increasingsamp le size.S u r v e y s o f r a r e e v e n t sNa tha n [10 ] and Nathan, Schmelz, and Kenvin [11]compared etticiencies of the de jure residence rule and acomposi te count ing rule in a natal i ty household sam plesurvey to es t imate the number of b ir ths . The de jureresidence rule links births to residences of their mothe rs,and the com posite counting rule links birth s to residencesof infants ' mothers , and maternal grandm others andaunts. The experiment was embedded in the Israel Labo rForce Survey during the firs t quarter of 1974, andrespondents retrospectively reported births that occurreddur ing 1973. Repor t ing bias was evaluated by a qual itycheck survey that interviewed residences of maternalgrandmothers and aunts when mothers in samplehouseholds reported births, and intervie wed reside nces ofmothers when maternal grandmothers or aun ts in samp lehouseholds reported births of grandch ildren or nieces ornephews.The var iance of the survey es t imate of the number ofbirths associated with the de jure residence rule isreduced by almost f i f ty percent by the maternalgrandmother /aunt composite count ing rule . The netreporting bias, however, is slightly sm alle r for th e de jurerule, +0.08 percent, than for the composite rule, +0.59percent. (Absolute values of the und er reporting andover reporting biases are substantially larger, 9.14percent and 9.73 percent, respectively for the c ompo siterule, than the 2.04 an d 2.12 p ercent, respectively for thede jure rule). The composite counting rule is moreefficient then the de jure rule to sam ple sizes up to about4,400 households for total births, and up to aconsiderably larger number of households for estimatesof b ir ths by demographic and geographic subdomains .Compared to the official demographic estimate, the dejure rule and the composite rule undercounted thenum ber of Is rael b ir ths in 1973 by almost 7 percent.Dual system estimators are often used to ad just for unde r


3/6

enumera t ion in surveys and censuses . The dual s y s t e mn e t w o r k e s t i ma t o r [ 2 1 8 ] i s the network s a mp l i n gv e r s i o n of the c lass ica l sampl ing dual system est imator[8] . The fo rmer uses a d i s jo in t count ing ru le that l inkseven ts to households by two independent count ing ru les(e.g. a de jure residence rule and a kin ship rule) , su chthat the same even ts a re no t l inked to the samehouse holds by bo th count ing ru les . The num ber o feven ts tha t would be repor ted by bo th count ing ru les i ses t imated by conduct ing qual i ty check surveys tha tin terv iew households e l ig ib le to repor t even ts by thecount ing ru le a l te rna tive to the one by wh ich those sameevents were originally repo rted in the survey.To my knowledge , dual system network es t imat ionp r o ced u r e s have not been f ie ld tested even though theyapp ear to have considerab le po t en t ia l fo r improvingdesign eff iciency of quali ty check surveys such as thepost enumeration survey (PES) to evaluate completenessof enumera t ion in decennia l censuses . Smal l p i lo t tes tsof PES designs based on ne twork sampl ing wereunder taken in p repar ing fo r the 1980 U.S. Census o fPopula t ion and Housing [9 , 22]. However , these PESpre tes ts o f ne twork sampl ing were under taken pr io r tothe developm ent o f dual system netwo rk es t imat ion .S u r v e y s o f r a r e p o p u l a t i o n sCzaja, Snowden, and Casady [4] com pare eff iciencies ofcanc er p revalence es t imates assoc iated wi th the de ju reres idence ru le l ink ing cancer pa t ien ts to the i r ownresidences and a composite counting rule l inking cancerpa t ien ts to the i r own res idences and those o f the i rch i ld ren . The exper iment invo lves 530 households o fwh ich 325 were households o f cancer pa tien ts se lec tedfrom cance r registr ies of two I l l inois hospitals, and 205we re I l lino is households o f ch i ld ren of the cancerpa t ien ts . Est imates o f under repor t ing b iases a reobtained by ma tching the canc er patients repo rted in thesurvey with the two can cer registers [3, 21] .Sampl ing var iance o f the cancer p revalence es t imatesbased on the de jure residence rule is reduced by abou t 50percen t by the ch i ld ren composi te count ing ru le. Un derrepor t ing b iases a re 11 .0 percen t and 14 .3 percen trespec t ive ly fo r de ju re res idence ru le and the ch i ld rencom posi te count ing ru le fo r a l l pa t ien t domains . Forcombined cancer si tes, the children composite rule ismore eff icient than the de jure rule for sam ple sizes up toabout 4200 households, and up to substantially largersam ple sizes for specif ic can cer si tes.Under repor t ing b ias var ies by sex , age and race o f

pa t ien t . For example , about 3 percen t and 7 percen trespec t ive ly o f whi te female cancer pa t ien ts are notreported at residences of patients and children. Th ecomparable under reporting biases for white male cance rpatient are 12 percen t and 16 percent, respectively. Forwhi te female cancer prevalence, the children compositerule is more eff icient than the de jure rule for samplesizes up to abou t 80,000 households.Household surveys of rare and e lus ive a nd /o r s ens i t ivep o p u l a t i o n sIf the rare population is also elusive or if the rareattr ibute is a sensit ive one, sample survey estimatesassociated with the de jure residence rule are vuln erableto large reporting biases as well as large sam pling errors.Un der e i ther o f these c i rcumstances , ne twork sampl ingoffers options that may be more eff icient than classicalsampl ing . For example , the l ike l ihood of enum era t ingelusive popula t ions , such as migran ts , nomads and thehomeless , may be be t te r i f they are enumera ted a t thefixed residences of knowledgeable close associates, suchas relative s and fr iends, than if enumera ted at elusivepers ons ow n residences. Similar ly, the l ikelihood ofenumerating populations w ith sensit ive attr ibutes may bebetter if they are enum erated at residences of fr iends andrelatives since that venue provides greater responseanonym ity , tha n the res idences o f persons w i th thesensit ive attr ibutes.S u r v e y s o f e l u s i v e p o p u l a t io n s

Decedents represent an elusive population inretrospective mortali ty household sample surveys usingthe de jure residence rule. Insti tutional deaths aremissed because they are n t l inked to any households bythe d e jure residen ce rule. Noninsti tutional deaths areoften missed because the decedents former householdsdissolve before the surveys are conducted.Si rken and Royston [ 24 ] compare e t t ic ienc ies o fmortali ty surveys using a de jure residence rule l inkingdecedents to their noninstitutional place s of reside nce atdeath, and a composite counting rule l inking decedentsto their former residences and to residences o f survivingspouses, siblings and children. In the survey experiment,which was conducted during 1975, respondentsretrospectively reported deaths that occurred during1974. Interviews were conducted at form ernonin sti tution al residences of decedents, and at thecurr ent residence s of the decedents surviving closerelative s for a sample of several hund red registereddeaths tha t occur red in Nor th Caro l ina dur ing 1974 .Under repor t ing b ias was assessed by match ing the


4/6

de aths r e por te d in the survey exper iment w ith f i les o fregistered deaths in North Carolina. A lthough d ecedentsat a l l ages are included in the exper iment , the f indingsreported here re fer to decedents, 65-84 years of age.The kinship com posi te count ing rule is uniformly moreeff ic ient than the de jure res idence rule for es t imat ingt h e number of nonins t i tu t ional deaths and even moreeff ic ient for es t imat ing the combined number ofinstitutional and noninstitution al deaths. Sam plingvar iance of the de jure res idence rule was reduced byabout 75 percent by the k inship composite ru le . Thefract ion of missed ins t i tu t ional and nonins t i tu t ionaldeaths was reduced by alm ost one half , from 29 percent,to 15 perc ent by the composite counting rule. The dejure rule missed all institutional deaths, whichrepresented about 22 perce nt of all deaths, and thecomposi te count ing rule missed about a th ird of theinstitutional deaths. Both counting rules failed toenumerate about 7 percen t of the noninstitutional de aths[19].

u r v e y s o f s e n s i t i v e p o p u l a t i o n sRittenhottse and Sirken [ 12] compa re efficiencies of thede jure residence rule linking heroin users to their ownresidences, and a comp osite counting rule link ing h eroinusers to their own residences and residences of their closefriends. The experim ent was embedded in a half sample(2250 household) o f the 1977 Nat ional Survey on DrugAbuse.

Es t imates of l i fe t ime heroin use prevalence aresubstantially higher for the friends counting rule (5.8percent) than for the de jure residence rule (1.3 percent) .How ever , samp ling var iances are a lmost twice as largefor the com posite rule than the de jure rule. Thissom ewh at surprising finding is due to extensiveclustering of heroin users within friendship networks andconsiderable variability in the heroin usersmultiplicities. Nevertheless, th e com posite friend s rule isfar more ef f ic ient than the de jure ru le assum ing thevalidity o f the composite rule s hig her lifetime heroin useprevalence estimate, wh ich was in close agreeme nt withexpert opinion on lifetime heroin use prevalence during1977.In this experimen t, abou t ten percent of the respondentsreported close friends that w ere heroin users, but almosta third of them failed to report the multiplicities of theirheroin user fr iends [5]. Therefore, the lifetime heroinprevalence was a lso es t imated by the hybr id networke s t i m a t o r [2 3] . This network es t imator u t i lizes al l

repor ts of heroin use repor table in com pliance with thefr iends composi te ru le , and ut i l izes m ult ip l ic i t ies whenh e r o i n u s e i s self reported, b u t d o e s n o t ut i l izemultiplicities wh en h eroin users are rep orted by friends.The hybr id network es t imate of l i fe t ime h e r o i nprevalence is 2.8 percent, or about mid wa y betw een themult ip l ic i ty es timate and the es t imate based on the dejure rule. Sampling errors are roughly 1.5 to 3 timeslarger for the hybr id es t imate than for the m ult ip l ic i tyestimate.My cur ios i ty about the potent ia l u t i l i ty of the f r iendscounting rule to estimate heroin use was initially a rousedby survey estimates of il l icit substance use tha t a re ba sedon respondents reports of the percentages o f the ir frien dsusin g ill icit substances. I ll icit substance use estima tesare substantially high er for reports of percentage friendsheroin use than self reports of heroin use. In the 1974Michigan Survey of Drug Abuse, for example, prevale nceestimates of about a half dozen ill icit drugs are 50 to 200percent higher based on reports of percentag e frien ds usethan for self reports of substance use [16]. On the o therhand, the prevalence estimates of several prescribeddrugs , including amphetamines , narcot ics andtranquilizers , are m ostly higher based on self reports tha nreports of percentage friends use. Th e co ntra stin g effectsof the count ing rules on the prevalence of prescr ibeddrugs and i l l ic i t drugs , sugges t that anonymity ofresponse provided by the friends rule enhanced thelikelihood of truthful response about il l icit dru g use.From a s ta t is t ical v iewpoint , the Michigan Surveyf indings are quite puzzl ing: averaging percentages off r iends repor ted as drug users , the es t imator in theMic higan Survey, is a biased estimator. I t wou ld be anunbiased es t imator i f and only i f f r iends of i l l ic it drugusers form closed networks in which f r iendship t iesbetween drug users and friends are reciprocal and neith erdrug users nor their fr iends have other fr iendship ties .There are multiplicity rules that form closed networks,but evidence is lacking tha t fr iends of drug users is oneof them. For exam ple, the s ib ling count ing rule and thematernal or paternal f irs t cousin counting rules aretransparent examples of c l o s e d c o u n t i n g ru les tha t fo rmclosed networks.T h e f u t u r e o f n e t w o r k s a m p l i n gThe future of network sampling is in terdiscipl inarysurvey methods research. Network sampling researchintersects the cognitive, behavioral, and statis ticalsciences . For example, fundamental knowledge aboutinformation networks l inking re la t ives and f r iends is


5/6

crit ical in designing surveys based o n ne twork samp ling,and know ledge ga ined about the robustness of theseinformat ion ne tworks f rom survey appl ica t ions ofnetwork sampling is potential ly valuable in sociologicalresearch. Also, fundamental knowledge about cognit iveaspects of information processing is essential indesigning complex questionnaires for household surveysusing ne twork sampl ing, and knowledge ga ined byobserving respondents respond to ne twork surveyquestionnaires is potentially valuable in cognitive sciencein s t imula t ing new areas of cogni t ive research (Si rkenand Schechter , in press) .

e f e r e n c e s

I l l Bi rnb aum , Z .W. Si rken, M.G. (1965).Design of Sample Surveys to Est imate thePreva lence of Rare Diseases : Th ree UnbiasedEst imates , Vital and Health Statis tics PHSPub lication No. 1, Series 2, No. 11. USGovernm ent Pr int ing Off ice , Washington.

[21 Casady, R.J . , Nathan, G. Si rken, M.G.(1985). Alternative dual system netwo rkestimators, International Statis tical Review 53,183-197.

[3] Czaja, R., Warnecke, R.B., Eastman, E.,Royston, P. , Sirken, M. Tuteur , D. (1984).Loca t ing pa t ients wi th ra re diseases us ingnetwork sampl ing: f requency and qua l i ty ofreporting, in Proceedings o f the Four thConference on Heal th Survey ResearchMethods . Public Health Publication No. 84-3346, Nat iona l Center for Heal th ServiceResearch, US Depar tment of Heal th and Hum anServices, pp. 311-324.

[4] Cza ja, R.F., Snow den, C.B. Casady, R.J.(1986) . Repo r t ing bias and sampl ing e r rors ina survey of a rare pop ulation u sing m ultiplicitycount ing rules . Journal o f the Amer icanStat ist ical Associat ion 81, 411-419.

[ 5 Fishburn, P .M. (1979). Heroin es t imatordevelopment. Un pub lished report subm itted tothe Nat iona l Ins t itute On Dru g Abuse .

[61 Hendricks, W .A., Searles, D.T . Ho rvitz, D.G .(1965). A com parison of three rules forassoc ia t ing fa rms and fa rmland wi th samplearea segments in agriculture surveys, inEst imation of Are as in Agr icul tural S ta t ist ics

[7]

[ 8

[91

[101

[111

[121

[13]

[141

[15l

Food and Agr icul ture . Organiza t ion of theUnited Nations, Rome, pp. 191-198.Kramm, E .R. , Crane , M.M., Si rken, M.G.Bro wn , M.L. (1962). A cystic f ibrosis pilots tudy in three New E nglan d s ta tes . Amer icanJournal o f Publ ic Heal th 52, 2041-2057.M arks , E . (1978). The role of dua l sys temestimation in Census evaluation, inDevelopment in Dual Sys tem Es t imation ofPopulation Size a nd Growth The U nivers ity ofAlberta Press. Edm onton , Alberta, Canad a.M arks, E. Ockay, C. (1978). A model fornetw ork (mu ltiplici ty) : est im ation of censusunder coverage , in American Stat is t icalAssociation 1978 Proceedings o f the Section onSurvey Research Meth od. American Statist icalAssociation, Alexandria.Natha n, G. (1976). An emp ir ical study ofresponse and sampling errors for mult iplici tyestimates with different coun ting rules, Journalof the Amer ican Stat is t ical Associat ion 71, pp803-815.Nathan, G., Schmeltz, O. Ken vin, J. (1977).Mu l t ipl ic ity Study of Ma r r iages and B ir ths inIsrael, Vital and Health Statis tics Series 2, No.78. DH EW Publ ica tion No. (PHS) 79-1352.US G overnment Pr int ing O ffice , W ashington.Rit tenhouse, J.D. Sirken, M.G . (1981). Anote on ne tworks , nomina t ions , andmultiplici ty, as contr ibutory to heroinestimation. Adminis trat ive Repor t Nat iona lInsti tute of Drug A buse, Dep artment Health andHum an Services, W ashington.Shim izu, I . Sirken, M.G . (1998). M ore onpopulation based establishment surveys, inAmerican Stat ist ical Associat ion 1998Proceedings o f the Section in Society Resea rchMethods in p r int .Sirken, M.G . (1970). Ho usehold surveys withmultiplicity, Journal of the Am erican Statis ticalAssociat ion 65, 257-266.Sirken, M.G . (1972). Varian ce comp onents ofmultiplicity estimators, Biometr ics 28, 869-873.


6/6

[ 6

[ 7]

[181

[191

I2O

[211

Si rken , M. G. (1975) . Evalua t ion and cr i tiqueof household sample surveys of substance abuse,in Alco hol a nd Other Drug Use and Abuse Inthe State of Mich igan Mi ch i gan Depar t m en t o fPubl ic Heal th , Lancin g pp 1-35 .S i rken , M.G. (1975). The count ing ru les t ra tegy in sample surveys , in A mer ica nStatist ical Association 1975 Proceeding s of theSection on Social Statist ics A m e r i c a nStat is t ical Associat ion, Alexandria, pp. 119-123.S i rken , M.G. (1979) . A dual sys tem networkes t imator , in Am erican S ta t is t ica l Associa t ion1979 Proceedin gs o f the Section on Sura yResearch Methods. American S ta t i s t i ca lAssocia t ion , A lexandr ia , pp . 340-342.S i rken , M.G. (1983) . Han dl ing m iss ion data byne t work s am p l i ng , i n Incomplete Data inSamp le Surveys Par t 111 Vol . 2 . Acade micPress , New Y ork , pp . 81-90 .S i rken , M. G. (1998) . Netwo rk Sampl ing , inEncyclopedia o f Biostatist ics .Volume 4. JohnW iley and Sons , pp 2977-2986.S i rken , M. , Roys ton , P . , Wamecke, R . ,Eas tm an, E . , Czaja , R . Monsees , D. (1980) .

[22

[231

I241

I25

Pi lo t of the nat ional cos t of cancer care survey,in Am erican S ta t is t ica l Associa t ion 1980Proceedings of the Section on Su rvey on SurveyResearch Methods pp 579-584.S i rken , M.G . , Graubard , B .L. , LaV al ley(1978) . Evalua t ion of Census populat ioncoverage by network surveys , in A mer ica nStatistical Association 1978 Procee dings o f theSect ion on Survey Research Methods pp 239-243.S i rken , M.G . Natha n , G. (1988) . Hybr idnetwork es t imators , in American S ta t is t ica lAssociation 1988 Proceedings of the Section onSurvey Research M ethods. American Stat is t icalAssocia t ion , A lexandr ia , pp . 459-461.Sirken, M.G . Royston, P.N. (1976). De signeffects in retrospect ive surveys, in A mer ica nStatist icalAssociation 1976 Proce edings o f theSection on Social Statist ics pp 773-777.Sirken, M .G., Shimizu, I. Jud kins, D. (1995 ).Populat ion based es tab l i shment surveys , inAm erica n Statist ical Associa tion 1995Proceedings of the Section on Su rvey Resea rchMethods. American S ta t i s t i ca l Associa t ion ,Alexandr ia , pp . 470-473.

a short history of network sampling

Documents