Multilevel Latent Class Models

TLDR: In this article, Parametric and non-parametric random-coefficient latent class models are proposed to modify the assumption that observations are independent, which can be used for the analysis of data collected with complex sampling designs, data with a multilevel structure, and multiple-group data for more than a few groups.

Abstract: The latent class (LC) models that have been developed so far assume that observations are independent. Parametric and non-parametric random-coefficient LC models are proposed here, which will make it possible to modify this assumption. For example, the models can be used for the analysis of data collected with complex sampling designs, data with a multilevel structure, and multiple-group data for more than a few groups. An adapted EM algorithm is presented that makes maximum-likelihood estimation feasible. The new model is illustrated with examples from organizational, educational, and cross-national comparative research.

Figures

Table 7. Posterior means of random effects and the corresponding proportion of postmaterialists for the 32 countries (Models 4 and 6, EVS data)

Figure 1: Graphical model associated with a LC model with a random-effect in the latent class distribution.

Table 3. Testing results obtained with the mathematical ability data

Table 2. Estimated parameter values of Models 4 and 5 (task-variety data)

Table 4. Estimated parameter values of parametric Model 10 (mathematical ability data)

Table 5. Testing results obtained with the EVS data

Full text

Tilburg University
Multilevel Latent Class Models
Vermunt, J.K.
Published in:
Sociological Methodology
Publication date:
2003
Document Version
Peer reviewed version
Link to publication in Tilburg University Research Portal
Citation for published version (APA):
Vermunt, J. K. (2003). Multilevel Latent Class Models.
Sociological Methodology
,
33
(1), 213-239.
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners
and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.
• You may not further distribute the material or use it for any profit-making activity or commercial gain
• You may freely distribute the URL identifying the publication in the public portal
Take down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Download date: 10. aug.. 2022

Pxowlohyho Odwhqw Fodvv Prghov
Mhurhq N1 Yhupxqw
Ghsduwphqw ri Phwkrgrorj| dqg Vwdwlvwlfv/ Wloexuj Xqlyhuvlw|
Dgguhvv ri fruuhvsrqghqfh=
Mhurhq N1 Yhupxqw
Ghsduwphqw ri Phwkrgrorj| dqg Vwdwlvwlfv
Wloexuj Xqlyhuvlw|
S1R1Er{ <3486
8333 OH Wloexuj
Wkh Qhwkhuodqgv
H0pdlo= M1N1YhupxqwCxyw1qo
Dffhswhg e| Vrflrorjlfdo Phwkrgrorj| +Qryhpehu 7/ 5335,

Pxowlohyho Odwhqw Fodvv Prghov
Devwudfw
Odwhqw fodvv +OF, prghov ghyhorshg vr idu dvvxph wkdw revhuydwlrqv duh lqghshqghqw1 Sdud0
phwulf dqg qrqsdudphwulf udqgrp0frh!flhqw OF prghov duh sursrvhg wkdw pdnh lw srvvleoh wr
uhod{ wklv dvvxpswlrq1 Wkh prghov fdq/ iru h{dpsoh/ eh xvhg iru wkh dqdo|vlv ri gdwd froohfwhg
zlwk frpsoh{ vdpsolqj ghvljqv/ gdwd zlwk d pxowlohyho vwuxfwxuh/ dqg pxowlsoh0jurxs gdwd iru
pruh wkdq d ihz jurxsv1 Dq dgdswhg HP dojrulwkp lv suhvhqwhg wkdw pdnhv pd{lpxp olnh0
olkrrg hvwlpdwlrq ihdvleoh1 Wkh qhz prgho lv looxvwudwhg zlwk h{dpsohv iurp rujdql}dwlrqdo/
hgxfdwlrqdo/ dqg furvv0qdwlrqdo frpsdudwlyh uhvhdufk1
4

Pxowlohyho Odwhqw Fodvv Prghov
4 Lqwurgxfwlrq
Lq wkh sdvw ghfdgh/ odwhqw fodvv +OF, dqdo|vlv +Od}duvihog/ 4<83> Jrrgpdq/ 4<:7, kdv ehfrph
d pruh zlgho| xvhg whfkqltxh lq vrfldo vflhqfhv uhvhdufk1 Rqh ri lwv dssolfdwlrqv lv foxvwhulqj
ru frqvwuxfwlqj w|srorjlhv zlwk revhuyhg fdwhjrulfdo yduldeohv1 Dqrwkhu uhodwhg dssolfdwlrq lv
ghdolqj zlwk phdvxuhphqw huuru lq qrplqdo dqg ruglqdo lqglfdwruv1 Dq lpsruwdqw olplwdwlrq ri
wkh OF prghov ghyhorshg vr idu lv/ krzhyhu/ wkdw wkh| dvvxph wkdw revhuydwlrqv duh lqghshqghqw/
dq dvvxpswlrq wkdw lv riwhq ylrodwhg1 Wklv sdshu suhvhqwv d udqgrp0frh!flhqwv ru pxowlohyho
OF prgho wkdw pdnhv lw srvvleoh wr uhod{ wklv dvvxpswlrq1
Udqgrp0frh!flhqwv prghov fdq eh xvhg wr ghdo zlwk ydulrxv w|shv ri ghshqghqw revhuydwlrqv
+Djuhvwl hw do1/ 5333,1 Dq h{dpsoh lv ghshqghqw revhuydwlrqv lq gdwd vhwv froohfwhg e| wzr0vwdjh
foxvwhu vdpsolqj ru orqjlwxglqdo ghvljqv1 D pruh wkhru| edvhg xvh ri udqgrp0frh!flhqwv prghov
wkdw lv srsxodu lq hogv vxfk dv hgxfdwlrqdo dqg rujdql}dwlrqdo uhvhdufk lv riwhq uhihuuhg wr dv
pxowlohyho ru klhudufklfdo prgholqj/ d phwkrg wkdw lv lqwhqghg wr glvhqwdqjoh jurxs0ohyho iurp
lqglylgxdo0ohyho hhfwv +Eu|n dqg Udxghqexvk/ 4<<5> Jrogvwhlq/ 4<<8> Vqlmghuv dqg Ervnhu/
4<<<,1 Dqrwkhu lqwhuhvwlqj dssolfdwlrq ri wkhvh phwkrgv lv lq wkh frqwh{w ri pxowlsoh0jurxs
dqdo|vlv/ vxfk dv lq furvv0qdwlrqdo frpsdudwlyh uhvhdufk edvhg rq gdwd iurp d odujh qxpehu ri
frxqwulhv +vhh/ iru h{dpsoh/ Zrqj dqg Pdvrq/ 4<;8,1
Lq d vwdqgdug OF prgho/ lw lv dvvxphg wkdw wkh prgho sdudphwhuv duh wkh vdph iru doo
shuvrqv +ohyho04 xqlwv,1 Wkh edvlf lghd ri d pxowlohyho OF prgho lv wkdw vrph ri wkh prgho
sdudphwhuv duh doorzhg wr glhuv dfurvv jurxsv/ foxvwhuv/ ru ohyho05 xqlwv1 Iru h{dpsoh/ wkh
suredelolw| ri ehorqjlqj wr d fhuwdlq odwhqw fodvv pd| glhu dfurvv rujdql}dwlrqv ru frxqwulhv1
Vxfk glhuhqfhv fdq eh prghoohg e| lqfoxglqj jurxs gxpplhv lq wkh prgho/ dv lv grqh lq
5

pxowlsoh0jurxs OF dqdo|vlv +Forjj dqg Jrrgpdq/ 4<;7,/ zklfk dprxqwv wr xvlqj zkdw lv
fdoohg d {hg0hhfwv dssurdfk1 Dowhuqdwlyho|/ lq d udqgrp0hhfwv dssurdfk/ wkh jurxs0vshflf
frh!flhqwv duh dvvxphg wr frph iurp d sduwlfxodu glvwulexwlrq/ zkrvh sdudphwhuv vkrxog eh
hvwlpdwhg1 Ghshqglqj rq zkhwkhu wkh irup ri wkh pl{lqj glvwulexwlrq lv vshflhg ru qrw/ hlwkhu
d sdudphwulf ru d qrqsdudphwulf udqgrp0hhfwv dssurdfk lv rewdlqhg1
Wkh sursrvhg pxowlohyho OF prgho lv vlplodu wr d udqgrp0frh!flhqwv orjlvwlf uhjuhvvlrq
prgho +Zrqj dqg Pdvrq/ 4<;8> Khghnhu dqg Jleerqv/ 4<<9> Khghnhu/ 4<<<> Djuhvwl hw do1/
5333,1 D glhuhqfh lv wkdw wkh ghshqghqw yduldeoh lv qrw gluhfwo| revhuyhg/ exw d odwhqw yduldeoh
zlwk vhyhudo revhuyhg lqglfdwruv1 Wkh prgho fdq/ wkhuhiruh/ eh vhhq dv dq h{whqvlrq ri d udqgrp0
frh!flhqwv orjlvwlf uhjuhvvlrq prgho lq zklfk wkhuh lv phdvxuhphqw huuru lq wkh ghshqghqw
yduldeoh1 Lw lv zhoo0nqrzq wkdw OF prghov fdq eh xvhg wr frpelqh wkh lqirupdwlrq frqwdlqhg
lq pxowlsoh rxwfrph yduldeohv +Edqghhq0Urfkh hw do1/ 4<<:,1
Wkh prgho lv dovr vlplodu wr wkh pxowlohyho lwhp uhvsrqvh wkhru| +LUW, prgho wkdw zdv
uhfhqwo| sursrvhg e| Ir{ dqg Jodv +5334,1 D frqfhswxdo glhuhqfh lv/ krzhyhu/ wkdw lq LUW
prghov wkh xqghuo|lqj odwhqw yduldeohv duh dvvxphg wr eh frqwlqxrxv lqvwhdg ri glvfuhwh1 Eh0
fdxvh ri wkh vlplodulw| ehwzhhq OF dqg LUW prghov +vhh/ iru h{dpsoh/ Khlqhq/ 4<<9,/ lw lv
qrw vxusulvlqj wkdw uhvwulfwhg pxowlohyho OF prghov fdq eh xvhg wr dssur{lpdwh pxowlohyho LUW
prghov1
Wkh lghd ri lqwurgxflqj udqgrp hhfwv lq OF dqdo|vlv lv qrw qhz= vhh/ iru h{dpsoh/ Tx/ Wdq/
dqg Nxwqhu +4<<9,/ dqg Ohqn dqg GhVduer +5333,1 Wkh prghov sursrvhg e| wkhvh dxwkruv duh/
krzhyhu/ qrw pxowlohyho prghov/ dqg wkhuhiruh frqfhswxdoo| dqg pdwkhpdwlfdoo| yhu| glhuhqw
iurp wkh prghov ghvfulehg lq wklv sdshu1 Dowkrxjk wkhuh lv qr rswlrq iru frpelqlqj OF vwuxf0
wxuhv zlwk udqgrp hhfwv lq wkh fxuuhqw yhuvlrq ri wkh JOODPP surjudp ri Udeh0Khvnhwk/
Slfnohv/ dqg Vnurqgdo +5334,/ wkh prgho L sursrvh wv yhu| qdwxudoo| lqwr wkh jhqhudo pxowlohyho
6

Frequently asked questions

Q1. What are the contributions in this paper?

If you believe that this document breaches copyright please contact us providing details, and the authors will remove access to the work immediately and investigate your claim.