University of Groningen

On the robustness of LISREL (maximum likelihood estimation) against small sample size andnon-normality.Boomsma, Anne

IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.

Document VersionPublisher's PDF, also known as Version of record

Publication date:1983

Link to publication in University of Groningen/UMCG research database

Citation for published version (APA):Boomsma, A. (1983). On the robustness of LISREL (maximum likelihood estimation) against small samplesize and non-normality. Groningen: s.n.

CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).

Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.

Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.

Download date: 02-04-2020

REFERENCES

Afifi, A.A. & Elashoff, R.M. (1966) Missing observations in multivariate

statistics I. Review of the literature. Journalof the American

Statistical Association , 61 , 595-604.

Aigner, D.J. & Goldberger, A.S. (Eds.) (1977) Latent variables in socio­

economie models . Amsterdam : North-Holland.

Anderson, T.W. (1958) An introduction to multivariate statistical analysis .

New York: Wiley.

Anderson, T.W. (1973) Asymptotically efficient estimation of covariance

matrices with linear structure. The Annals of Statistics , 1 , 135-

141.

Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H. &

Tukey,J.W.(1972) Robust estimates of location . Survey and advances .

Princeton, Nèw Jersey: Princeton University Press .

Andrews, D.F. ,Gnanadesikan, R. & Warner, J.L. (1973) Methods for assessing

multivariate normality. In P.R. Krishnaiah (Ed.) ,Multivariate analysis ­

III . New York: Academic Press, 95-116.

Barnett, V. (Ed.) (1981) Interpreting multivariate data . Chichester: .,Wiley.

Barnett, V. & Lewis, T. (1978) Out liers in statistical data . Chichester:

Wiley.

Bartholomew, D.J. (1980) Factor analysis for categorical data. Journal

of the Royal Statistical Society, Series B, 42 , 293-321 . (with

discussion )

Beale, E.M.L. & Little, R.J.A. (1975) Missing values in multivariate analysis.

Journalof the Royal Statistical Society, Series B, 37 , 129-145.

Bentler, P.M. (1976) Multistructure statistical model applied to factor

analysis. Multivariate Behavioral Research , 11 , 3-25.

BentIer, P.M. (1980) Multivariate analysis with latent variables: Causal

modeling. Annual Review of Psychology, 31 , 419-456.

Bentler, P.M. & Bonett, D.G. (1980) Significance tests and goodness of

fit in the analysis of covariance structures. Psychological Bulletin ,

88 , 588-606.

BentIer, P.M. & Weeks, D.G. (1979) Interrelations among models for the

analysis of moment structures. Multivariate Behavioral Research , 14 ,

169-186.

208

Bentler, P.M. & Weeks, D.G. (1980) Linear structural equations with latent

variables. Psychometrika , 45 , 289-308.

Bickei, P.J. (1976) Another look at robustness: A review of reviews and

some new developments. Scandinavian Journalof Statis t i cs, 3, 145-

168.

Bielby, W.T. & Hauser, R.M. (1977) Structural equation modeis. Annual

Review of Sociology , 3, 137-161.

Blok, H. & Saris, W.E. (1980) Relevante variabelen bij het doorverwijzen

na de lagere school; een structureel model. Tijdschrift voor Onder­

wijsresearch , 5, 63-79.

Bock, R.D. (1960) Components of varianee analysis as a structural and

discriminal ana lysis for psychological tests. The British Journal

of Statistical Psychology , 13, 151-163.

Bock, R.D. & Bargmann, R.E. (1966) Analysis of covariance structures.

Psychometrika , 31 , 507-534.

Bock, R.D. & Lieberman, M. (1970) Fitting a response model for n dichotomously

scored items. Psychometrika , 35 , 179-197.

Boomsma , A. (1980~ Note on robustness studies of maximum likelihood factor

analysis. Heymans Bulletin , HB- 80- 4?? - EX, Rijksuniversiteit Groningen,

Psychologische Instituten.

Boomsma, A. (1980b) The robustness of LISREL against non-normality. In

M.M. Barritt & D. Wishart (Eds.). COMPSTAT 1980 . proceedings in

computational Statistics . Wien: Physica-Verlag, 174-180.

Boomsma, A. (1982 a) Empirica l percentage points of the approximate W'­

test for norma lity. (unpublished)

Boomsma, A. (1982b) Detailed results of a Monte Carlo study on the robustness

of LISREL against small sample size and non-normality. Heymans Bulletin ,

HB- 83- 623- EX, Rijksuniversiteit Groningen, Psychologische Instituten.

Boomsma, A. (1982~ The robustness of LISREL against small sample sizes

in factor analysis models. In K.G. Jöreskog & H. Wold (Eds.), Sy stems

under indirect observation : Causal i t y, structur e , pr edi ction (Part I),

Amsterdam: North-Holland, 149-173.

Boomsma, A. (1982 cl) Facts and failures of Monte Carlo work with LISREL.

Heymans Bulletin , HB- 82- 5??- EX, Rijksuniversiteit Groningen, Psycho­

logische Instituten. (submitted for publication)

Bowman, K.O., Beauchamp, J.J. & Shenton, L.R. (1977) The distribution of

209

the t-statistic under non-normality. International Statistical Review ,

45 , 233-242.

Box, G.E.P. (1953) Non-normality and tests on variances. Biometrika , 40 ,

318-335.

Bradley, J.V. (1968) Distribution- f ree statistical tests . Englewood Clif f s,

New Jersey : Prentice Hall.

Bradley, J.V. (1977) A common situation conduc i ve to bizarre distribution

shapes. The American Statistician , 31 , 147-150.

Bradley, J.V. (1978) Robustness? The British Journa~ of Mathematica~ and

Statistica~ Psycho~ogy , 31 , 144-152.

Browne, M.W. (1968) A comparison of factor ana l ytic techniques. Psychometrika ,

33 , 267-334.

Browne, M.W. (1974) Generalized least squares estimators in the analysis

of covariance structures. South African Statistica~ Journa~ , 8 , 1-

24.

Browne, M.W. (1982) Covarianc e structures. In D.M. Hawkins (Ed.), Topics

in app~ied mu~tivariate ana~ysis . Cambridge: Cambridge University

Press, 72-141.

Campbell, N.A. (1980) Robust procedures in multivariate analysis I: Robust

covariance estimation. App~ied Statistics , 29 , 231-237.

Carroll, J.B. (1961) The nature of the data, or how to choose a correlation

co.efficient. Psychometrika , 26 , 347-372.

Chen, C.F. (1981) The EM approach to the multiple indicators and multipl e

causes model v~a the estimation of the latent variable. Journa~ of

the American Statistica~ Association , 76 , 704-708.

Christoffersson, A. (1975) Factor analysis of di chotomized variables.

Psychometrika , 40 , 5-32.

Christoffersson, A. (1977) Two-step weighted least squares factor analysis

of dichotomized variables. Psychometrika , 42 , 433-438.

Cox, D.R. & Hinkley, D.V. (1974) TheoreticaZ statisti cs . London: Chapman

& Hall.

Cox, D.R. & Small, N.J.H. (1978) Testing multivariate normality. Biometrika ,

65 , 263-272.

Cramér, H. (1946) MathematicaZ methods of statistics . Princeton: Princeton

University Press.

Davidon, W.C. (1959) Variable metric method for minimiz~tion. A. E. C. Reeearch

and DeveZopment Report , ANL- 5990 (ReJ) . ) .

210

Dempster , A.P., La ird, N.M. & Rubin, D.B. (1977) Maximum likelihood from

incomplete data via the EM algorithm. JournaZ of the RoyaZ Stati sticaZ

Society , Series B, 39 , 1-38 . (with discussion)

De Pijper, W.M. & Saris, W.E. (1976) Pad- analyse of de LISREL- procedure

voor paneldata? Mens en Maatschappij, 51 , 398-417 .

Devlin , S . J . , Gnanadesikan, R. & Kettenring, J.R . (1975) Robus t estimation

and out lier detection with correlation coefficients . Biometrika ,

52 , 531-545.

Dijkhuizen, A. A. (1977) Klassieke econometrische methoden voor het schatten

van de structuurparameters in een padanalytisch model. Rotterdamse

Medede~ingen no . 23 , Rotterdam: Project Onderwijs en Sociaal Milieu .

Dijkhuizen, A. A. (1978) LISREL- procedure. Mathematisch-statistische analyse

van lineaire structurele vergelijkingen modellen met latente varia­

belen. Rotterdamse Mede~ingen no . 34 , Rotterdam: Project Onderwijs

en Sociaal Milieu.

Dijkstra, T. K. (1981) Latent variab~es in ~inear stochasti c models .

Ref~ections on "maximum ~ike~ihood " and "partia~ leas t squares "

methods . Groningen. (unpublished doctoral dissertation)

Dijkstra, T.K . (1983) Same comments cn maximum li.kE'lihood and partial

least squares methods. Journalof Econometri cs . (in press)

Duncan, G. T. & Layard, M.W.J. (1973) A Monte-Carlo study of asymptotically

robust tests for correlation coefficients . Biometrika, 60, 551 - 558 .

Duncan , O. D. , Haller, A.O . & Portes, A. (1968) Peer influences on

aspirations: A reinterpretation. The Amer ican Journa~ of Sociology,

74 , 119- 137 .

Efron, B. (1979) Bootstrap methods: Another look at the jackknife . The

Anna~s of Stati stics , 7, 1-26 .

Eiting , M.H. (1981) De cognitie van muzikale eenheden, systemen en

transformaties (zesde deelrapport). Intern ICO- rappor t , Universiteit

van Amsterdam .

Eiting , M. H. & Mellenbergh, G.J. ( 1980 ) Testing covariance matrix hypotheses :

An example from the measurement of musical abilities. Mu l tivar i ate

Behavior al Research , 15, 203-223 .

Everitt, B. (1978) Graphical techni ques f or multivariate dat a . London:

Heinemann .

Finkbeiner, C. (1979) Estimation for the multiple common fac t or model when

data are missing . Psychometrika , 44, 409- 420 .

Fleishman . A. I . ( 1978) A method fo r s i mulat ing non- norma l di s t r i but ions.

21 1

Psychometrika , 43 , 521-532.

Fletcher, R. & Powell, M.J.D. (1963) A r apidly convergent descent me thod

for minimization. The Co~puter Journal , 6 , 163-168.

Frane, J.W. (1975) A new BMD program for the description and estimation

of missing data. Proceedi ngs of Statistical Computing Section , The

Amer ican Statistical Association , 110-114.

Frane, J.W. (1976) Some simple procedures for handling missing data in

multivariate analysis. Psychometrika , 41 , 409-415.

Fridshal, D. & Posten, H.O. (1966) Bibliography on statistical robustness

and related topics. Research Report no . 16 , University of Connecticut,

Department of Statistics.

Gadourek, I. (1982) Social change as rede f inition of roles . A study of

structural and causal relati onships in The Netherlands of the

'seventies '. Assen: Van Gorcum.

Geary, R.C. (1947) Testing for normality. Biometrika , 34 , 209-242.

Geweke, J.F. & Singleton, K.J. (1980) Interpreting the likelihood r a tio

statistic in factor models when sample size is small. Journalof t he

Amer ican Statistical Association , 75 , 133-137.

Gifi, A. (1981) Non- linear multivariate analysis . University of Leiden,

Department of Data Theory.

Gleason, T.C. & Staelin, R. (1975) A proposal for handling missing data.

Psychometrika , 40 , 229-252.

Gnanadesikan, R. (1977) Methods for statistical data analysis of multivariate

observations . New York: Wiley.

Gnanadesikan, R. & Kettenring, J.R. (197 2) Robust estimates, residuals,

and out lier detection with multiresponse data. Biometrics , 28 , 81-

124.

Goldberger, A.S. & Duncan, O.D. (Eds.) (1973) Structural equation models

in the social sciences . New York: Seminar Press.

Govindarajulu, Z. & Leslie, R.T. (1972) Annnotated bibliography on robustness

studies of statistical procedures. Vital and Health Statistics , Data

Evaluation and Methods Research , Series 2, no . 51 , Rockvilie, Maryland:

U.S. Department of Health, Education, and Welfare.

Gruvaeus, G.T. & Jöreskog, K.G. (1970) A comp ut e r progr am f or mi nimiz ing

a function of several variables. Research Bulletin 70- 14 , Princ e ton,

New Jersey: Educational Testing Service.

212

Hägglund, G. (1982) Factor analysis by instrumental variables methods.

Psychometrika , 47, 209-222.

Harter, H.L. (1961) Expected values of norma l order statistics. Biometrika ,

48 , 151-165.

Hartley, H.O. (1977) Solution of statistical distribution problems by

Monte Carlo methods . In K. Enslein , A. Ra lston & H.S. Wilf (Eds.),

Statistical methods for digital computers . New York: Wiley, 16-34.

Hatch, L.O . & Posten, H.O. (1966) Robustness of the Student-procedure:

A survey. Research Report no . 24 , University of Connecticut,

Department of Statistics.

Hatch, L . O. & Posten, H.O. (1969) A quantit a tive approach to robustness.

Research Report no . 42 , University of Connec ticut, Department of

Statistics .

Havlicek, L.L. & Peterson, N.L. (1977) Effect of the violation of assumptions

upon significance leve ls of the Pearson r. Psychological Bulletin ,

84 , 373-377.

Hay s, W.L. (1970) Statistics , London: Holt, Rinehart & Winston.

Henrysson, S . (1950) The significance of f ac tor loadings . Lawley' s test

examined by artificial samples. The British Journalof Psychology ,

Statistical Section , 3, 159-165.

Hoadley, B. (1971) Asymptotic properties of max~mum likelihood estimators

for the independent not identically distributed case . The Annals of

Mathematical Statistics , 42 , 1977-1991.

Hogg , R.V. (1974) Adaptive robust procedures: A partial review and some

suggestions for future applications and theory. Journalof the

American Statistical Association , 69 , 909-927 .

Ho gg , R.V. (1979a) Statistical robustness: One v~ew of its use ~n appli­

cat i ons today. The American Statistician , 33 , 108-115.

Ho gg , R.V. (1978b) An introduction to robust estimation. In R.L. Launer

& G.N. Wilkinson (Eds.), Robustness in statistics . New York: Academic

Press, 1-17.

Horn, J .L. & McArdle, J .J. (1980) Perspectives on mathematical/statistical

model building (MASMOB) in research on aging. In L.W. Poon (Ed.),

Aging in the 1980 ' s : Psychological issues . Washington, D.C.: American

Psychological Association, 503-541.

Huber, P.J. (1972) Robust statistics : A review. The Annals of Mathematical

Statistics , 43 , 1041-1067.

213

Huber, P.J. (1977a) Robust covarlances . In 5.5. Gupta & D.S. Moore (Eds.),

Statistical decision theory and related topics - II . New York: Academic

Press, 165-191.

Huber, P.J. (1977b) Robust statistical procedures .Philadelphia, Pennsylvania:

Society for Industrual and Applied Mathematics.

Huber, P . J . (1981) Robust statistics . New York: Wiley .

Hyrenius, H. , Adolfsson, I., et al. (Eds.) (1964) Selected bibliography on

non-normality, Publication no . 12 ,

of Statistics.

University of Göteborg , Department

IMSL (1982) IMSL Library . Re f erence manual (4 vols.; 9th ed.). Houston,

Texas: International Mathematical and Statistical Libraries.

Jöreskog, K.G. (1967) Some contributions to maximum likelihood factor

analysis. Psychometr ika , 32 , 443-482.

Jöre skog, K.G. (1969) A general approach to confirmatory maximum like lihood

factor analysis . Psychometrika , 34, 183-202.

Jöreskog, K.G. (1970) A general method for analysis of covariance structure s .

Biometrika , 5 7, 239-251.

Jöreskog, K.G. (1971) Simultaneous factor analysis ln several populations.

Psychometr ika , 36 , 409-426.

Jöreskog , K. G. (1973a) Analysis of covariance structures. In P . R. Kri shnaiah

(Ed.), Multivariate analysis - III . New York: Academic Press, 263-285 .

Jöreskog , K. G. (1973b) A general method for estimating a linear struc tural

equation system. In A.S. Goldberger & a.D. Duncan (Eds.), Structural

equation models in the social sciences . New York: Seminar Press, 85-

112.

Jöreskog, K.G. (1974) Analyzing psychological data by structural analysis

of covariance matrices. In D.H. Krantz, R.e. Atkinson, R.D. Luce &

P . Suppes (Eds.), Contemporar y developments i n mathemati cal psychology

(Vol. 11). San Francisco: Freeman, 1-56.

Jöreskog, K.G. (1977) Structural equation models in the social sciences :

Specification, estimation and testing. In P.R . Krishnaiah (Ed.),

Applications of statistics . Amsterdam : North-Holland, 265-287.

Jöreskog, K. G. (1978) Structural analysis of covariance and correlation

matrices. Psychometri ka , 43 , 443-477.

Jöreskog, K.G. (1979) Statistical estimation of structural models in

longitudinal-developmental investi gations . In J . R. Nesselroade &

214

P.B . Baltes (Eds . ), Longi t udina l res earch in the study of behavior

and development . New York : Academic Press, 303-352 .

Jöreskog, K.G. (1981) Analysis of covariance structures . Scandi navian

JournaZ of Statistics , 8, 65-92. (with discus SiON

Jöreskog, K.G. (1982) The LISREL approach to causal model- building in the

social sciences. In K.G. Jöreskog & H. Wold (Eds.),Sys tems under

indir ect observation : Causality , structure , pr edi ction (Part I).

Amsterdam: North-Holland, 81-99.

Jöreskog, K.G. & Goldberger, A.S. (1972) Factor analysis by general i zed

least squares. Psychometrika , 37 , 243-260 .

Jöreskog, K.G. & Goldberger, A.S . (1975) Estimation of a model with multiple

indicators and multiple causes of a single latent variabie. Journal

of the American Statistical Associ ation , 70 , 631-639.

Jöreskog, K. G., Gruvaeus, G.T. & Van Thillo, M. (1970) ACOVS - A general

computer progr am for ana l ysis of covariance structures. Research Bulletin

70- 15 , Princeton, New Jersey : Educational Testing Service .

Jöreskog, K.G . & Sörbom, D. (1976a) Statistical models and methods for

test-retest situations . . In D. N.M. de Gruijter & L.J.Th. van der Kamp

(Eds.), Advances in psychological and educational measurement . London :

Wiley, 135-157.

Jöreskog, K. G. & Sörbom, D. (1976b) LISREL - Esti mation of l i near s t ructural

equati on systems by maximum likeli hood methods . Chicago, Illinois:

International Educa tional Services.

Jöreskog, K. G. & Sörbom, D. (1977) Statistical models and methods for

analysis of longitudinal data. In D. J . Aigner & A.S. Goldberger (Eds . ),

Latent variables in socio- economie models .Amsterdam : North-Holland,

285- 325 .

Jöreskog, K. G. & Sörbom, D. (1978) LISREL IV. A general computer progr am

f or esti mation of linear structural equation systems by maximum like­

l ihood methods . User ' s guide . Un i versity of Uppsala, Department of

Statistics.

Jöreskog, K. G. & Sörbom, D. (1979) EFAP: Exploratory fac tor ana lysis program .

User's guide . Chicago, Illinois: International Educational Services .

Jöreskog, K.G. & Sörbom, D. (1981) LISREL V. Analysis of structural relation­

ships by maximum likelihood and least squares methods . Research Report

81 - 8 , University of Uppsala, Department of Statistics .

215

Jöreskog, K. G. & Sörbom, D. (1982) Brief information on LISREL, versions IV,

v and VI. University of Uppsala, Department of Statistics. (unpublished)

Jöreskog, K. G. & Van Thillo, M. (1973) LISREL - A general computer program

for estimating a linear structural equation of unmeasured variables.

Research Report 73- 5 , University of Uppsala, Department of Statistics .

Jöreskog, K.G. & Wold, H. (1982) The ML and PLS techniques for modeling

with latent variables : Historical and comparative aspects. In K.G .

Jöreskog & H. Wold (Eds.), Systems under indirect observation : CausaZity ,

structure , prediction (Part I) . Amsterdam : North- Holland, 263-270.

Keesling, J.W. (1972) Maximum ~ike~ihood approaches to causa~ f~ow ana~ysis .

Chicago, Illinois: University of Chicago, School of Education.

(unpublished doctoral dissertation)

Kelderman , H. ,Mellenbergh, G. J . & Elshout, J . J . (1981) Guilford ' s facet

theory of intelligence : An empirical comparison of modeis . Mu~tivariate

Behaviora~ Research , 16 , 37- 62.

Kendall, M.G. & Stua"rt, A. (1958) The advanced theory of statistics (Vol. 1).

London: Griffin .

Kendali, M. G. & Stuart, A. (1973) The advanced theory of statistics (Vol.2 ;

3rd. ed . ) . London: Griffin.

Kleijnen , J.P . C. (1974- 1975) Statis tica~ techniques in simu~ation (in

two parts). New York: Dekker .

Knol, H. R. (1980) Dominante houdingspatronen in een p~uriforme samen~eving .

Een ~ande~ijk empirisch onderzoek naar attitude- con f iguraties . Groningen.

(unpublished doctoral dissertation)

Kowalski, C. J . (1972) On the effects of non-normality on the distribution

of the sample product- moment correlation coefficient. App~ied Statistics ,

21 , 1- 12.

Kraemer, H. C. (1980) Robustness of the distribution theory of the product

moment correlation coefficient . Journa~ of Educationa~ Statistics ,

5 , 115-128 .

Krane , W. R. & McDonald, R.P . (1978) Scale invariance and the factor analysis

of correlation matrices. The Bri tish Journa~ of Mathematical and Stat­

istica~ Psycho~ogy , 31 , 218 - 228 .

Kshirsagar,A .M. (1959) Bartlett decomposition and Wishart distribution.

The Anna~s of Mathematica~ Stati stics , 30 , 239-241 .

Layard, M. W.J. (1972) Large sample tests for the equality of two covariance

216

matrices. The Annals of Mathematical Statistics , 43 , 123-141.

Layard, M.W.J. (1974) A Monte Carlo comparison of tests for equality of

covariance ma trice s . Biome tl?i ka , 61 , 461-465.

Lawley, D. N. (1940) The estimation of factor loadings by the method of

max imum likelihood. Proceedings of the Royal Society of Edinburgh ,

Series A, 60 , 64-82.

Lawley, D.N. & Maxwe ll, A. E. (1971) Factor analysis as a statistical method

(2nd. ed . ). London: Butterworth.

Lawley, D.N. & Swanson, Z. (1954) Tests of significance in a factor analysis

of artificial data. The British Journalof Statistical Psychology ,

7, 75-79.

Lee, S.Y. (1980) Estimation of covariance structure models with parameters

subject to functional restraints. Psychometrika , 45 , 309-324.

Lee, S.Y. & Jennrich, R.I. (1979) A study of algorithms for covariance

structure analysis with specific comparisons using factor analysis.

Psychometrika , 44 , 99-113.

Lee, S.Y. & Tsui, K.L. (1982) Covariance structure analysis in several

populations . Psychometrika , 47 , 297-308.

Lewis, P.A.W., Goodman, A.S. & Miller, J.M. (1969) A pseudo-random number

generator for the System/360. IBM Systems Journal , 8, 136-146.

Li, S.T. & Hammond, J .L. (1975) Generation of pseudorandom numbers with

specified univariate distributions and correlation coefficients.

IEEE Tran sactions on Systems, Man , and Cyber netics, SMC- 5, 557-561.

Linn, R. L. (1968) A Monte Carlo approach to the number of factors problem.

Psychometrika , 33 , 37-71.

Lord, F.M . & Novick, M.R. (1968) Statistical theor ies of mental test scores.

Reading, Massachusetts: Addison-Wesley .

Malkovich, J . F. & Afifi, A.A. (1973) On tests for multivariate normality.

Journalof the American Statis t i cal Associati on , 68 , 176-179.

Mallows,C.L . (1979) Robust methods - Some examples of their use. The

American Statistician , 33 , 179-184.

Marazzi, A. (1980a) ROBETH: A subroutine library for robust statistical

procedures. In M.M. Barritt & D. Wishart (Eds.), COMPSTAT 1980 .

Proceedings in Computational Stati stics . Wien: Physica- Verlag, 577-583.

Marazzi, A. (1980b) Robust affine invariant covariances in ROBETH. ROBETH

Document no.3. Research Repor t no . 24, Eidgenössische Technische Hoch­

schule, Zürich, Fachgruppe für Statistik.

217

Mardia, K.V. (1974) Applications of some measures of multivariate skewness

and kurtosis in t es ting normality and robustness studies. Sankhya : The

Indian JournaZ of Statistics , Series E, 36 , 115-128.

Maronna, R.A. (1976) Robust M-estima tors of multivaria te Ioca tion and scatter.

The Annals of Statistics , 4 , 51-67.

Massey , F . J . (1951) The Kolmogorov-Smirnov test for goodness of fit . Journal

of the American Statistical Association , 46 , 68-78.

Mattsson, A., DIsson, U. & Rosén, M. (1966) The maximum likelihood method ~n

fac t or analysis with special consideration to the problem of improper

solutions . Research Report , University of Uppsala, Department of

Statistics.

McArdle, J.J. (1979) A systematic v~ew of moment structure modeling : The RAM

theory. Paper presented a t the Psychometrie Society Meetings, Monterey,

California, June 7.

McArdle, J.J . (198D) .Causal modeling applied to psychonomie systems

simulation. Behavior Research Methods and Instrumentation , 12 ,

193-209.

McArdle, J . J . & McDona ld, R. P . (1980) A simple algebra ic representation

of moment structures . (unpublished)

McDonald, R.P. (1978) A simple comprehensive model for the analysis

of covariance structures. The British JournaZ of Mathematical

and Statistical Psychology , 31, 59-72.

McDonald, R.P. (1979) The structural analysis of multivariate data:

A sketch of a general theory. Multivariate Behavioral Research , 14 ,

21 -38.

Meijnen, G.W. (1977) Maatschappelijke achtergronden van intellektuele

ontwikkeling. Een empirisch onderzoek naar de invloed van de status­

specifieke opvoeding op de ontwikkeling van intelligentie en leer­

prestaties . Groningen: Wolters-Noordhoff. (doctoral dissertation)

Mellenbergh, G.J. (1980) Modellen te pas of te onpas? Tijdschrift voor

Onderwijsresearch , 5, (extra nummer), 48-53.

MilIer, R.G. (1974) The jackknife - A review. Biometrika , 61, 1-15.

Mooijaart, A. (1981) Factor analysis for ordered categorical variables

with normally distributed process variables. MT 08- 81 , Rijksuniver­

siteit Leiden, Subfaculteit der Psychologie .

Morrison, D.F. (1976) Multivariate statistical methods (2nd. ed.) . New York :

McGraw-Hill .

218

Muirhcad , R. J. & Waternaux, C. M. (1980) Asymptot i c distributions in canoni cal

correlation analysis and other multivaria t e procedures for nonnormal

populations. B{ometrika , 67 , 31-43.

Muthén , B. (1978) Contributions to factor analys i s of dicho tomous variab l es.

Psychometrika , 43, 551-560.

Muthén, B. (1982.a) Some categorical variable models with latent variables .

In K.G. Jöreskog & H. Wold (Eds.), Systems under indirect observation :

Causality , structure , prediction (Part I) . Amsterdam : North­

Holland, 65-79.

Muthén, B. (1982b) Structural equat i on modeling with ordered categorical

and cont inuous la t en t variable indicators. Paper presented at

the Jo int Mee tings of the Psychometrie Society and the Classification

Soc i ety, Montreal , May 30 - June 2 .

Norris , R. C. & Hjelm, H. F . (1961)Nonnormality and produc t moment correlation .

Journalof Experimental Education , 29 , 26 1-270.

Odell ., P .L. & Feiveson, A. H. (1966) A numerical procedure to generate

a sample covariance matrix . Journalof the American Statistical

Association , 61 , 199-203 .

Olson, C.L. (1974) Comparative robustness of SLX t es ts in multivariate

analysis of variance. Journalof the American Statistical Association ,

69, 894-908.

Olson, C.L . (1976) On choosing a test statistic in multivariate analysis

of variance . Psychological Bulletin , 83 , 579-586.

Olsson, U. (1978) Some data analytic problems in models with latent

variables . Research Report 78- 8 , University of Uppsala, Department

of Statistics.(unpublished doctoral dissertation)

Olsson, U. (1979a) Maximum likelihood estimation of the polychoric

correlat i on coefficient . Psychometrika , 44 , 443-460.

alsson, U. (157gb) On the robustness of factor analysis against c rude

classification of the observations. Multivariate Behavioral

Research , 14, 485-500.

Olsson , U., Drasgow, F. & Dorans, N.J . (1982) The polyserial correlation

coefficient . Psychometrika , 47, 337 - 347.

armel, H. (1980) Moeite met leven of een moeilijk leven . Een vervolg­

onderzoek naar de invloed van psychosociale belasting op het

welbevinden van driehonderd Nederlanders . Groningen: Konstapel .

219

(doctoral dissertation)

Pearson, E.S. & Please, N.W. (1975) Relation be twe en the shape of

the population distribution and the robustness of four s imple

test statistics . Biometrika , 62 , 223-241 .

Pearson, K. (1895) Contributions to the ma thematica l theory of evolu tion -

11. Skew var i a tion in homogeneous material . PhiZosophicaZ Transactions

of the RoyaZ Society of London , Series A, 186 , 343-414.

Pearson, K. (1901) Mathematical contributions to the theory of evolu tion -

VII. On the corre l at i on of characters not qu antitatively measurable.

PhiZosophicaZ Transactions of the RoyaZ Society of London , Series

A , 195 , 1-47.

Pearson, K. (1913) On the measurement of the influence of "broad

categories" on correlation. Biometrika, 9, 115-139.

Peschar, J . P. (1975) MiZieu , schooZ en beroep . Een achteraf- experiment

over de periode 1958- 1973 naar de invZoed van het sociaaZ milieu

op schooZ- en beroepsZoopbaan . Groningen: Tjeenk-Willink. (doctoral

dissertation)

Peschar, J.P . (1977) Kanttekeningen bij recent Amerikaans onderzoek

naar de stratificatie in school en beroep. BuZZetin van de Vakgroep

Methoden en Technieken nr . 22 , Rijksuniversiteit Groningen,

Sociologisch Instituut.

Posten, H.O. (1969) Supplement to "bibliography on statistical robustness

and related topics". Research Report no . 46 , University of Connectieut,

Department of Sta tistics. (see D. Fridshal & H.O. Posten, 1966)

Rao, C.R. (1973) Linear statisticaZ inference and its appZications (2nd. ed.).

New York: Wiley .

Royston, J . P. ( 1982a) An extension of Shapiro and Wilk's W test for

normality to large samples. AppZied Statistics , 31 , 115-124.

Royston, J.P. (1982b) Algorithm AS 181. The W test for norrnality.

AppZied Statistics , 31 , 176-180.

Saris, W.E. (1979. ~ Methods and techniques for the anaZysis of survey

data with measurement error . Amsterdam . (unpublished doctoral

dissertation)

Saris, W.E. (1979b) Introduct~on to the use of Zinear structuraZ

equation modeZs in non- experimentaZ research . Vrije Universiteit

Amsterdam, Vakgroep Methoden en Technieken.

220

, ....

Saris, W.E. (1980) Linear struc tural rela tionship s . QuaLity and Quantity ,

14 , 205-224.

Scheffé, H. (1959) The anaLysis of variance . New York: Wiley .

Scott, J.T.Jr. & Fleishman, A. (1978) Statistical analysis of the goodness

of classica l f actor analysis regression (CFAR). BuLLetin 759 , University

of Illinois, Urbana-Champaign, Agric ultura l Experiment Station.

Shapiro, S.S . & Franc i a , R.S. (1972) An approxima te analysis of varianee

t est for normality . JournaL of the American StatisticaL AS$ociation, 67 ,

215-216.

Shapiro, S.S. & Wilk, M.B. (1965) An analysis of varianee test for normality

(complete samples). Biometrika , 52 , 591-611.

Shapiro, S.S., Wilk, M.B . & Chen, H. J. (1968) A comparative study of various

tests for normality. Journalof the American StatisticaL Association ,

63 ,1343-1372.

Shaw, N.H. (1978) Robustness of maximum likelihood factor analysis to

nonrandomness. Dissertation Abstracts International A, 39 (4), 2208.

Silvey, S.D. (1975) Statistical in f erence . London: Chapman & Hall.

Sörbom, D. (1974) A genera I method for studying differences in factor

means and factor structure between groups. The British Journalo f

MathematicaL and Statistical Psychology , 27, 229-239 .

Sörbom, D. (1976) A statistical model for the measurement of change in

true scores. In D.N. M. de Gruijter & L.J.Th. van der Kamp (Eds.),

Advances in psychological and educational measurement . London: Wiley,

159-170.

Sörbom, D. (1978) An alternative to the methodology for analysis of

covariance. Psychometrika , 43 , 381 - 396.

Sörbom, D. (1982) Structural equation mdoels with structured means. In

K.G. Jöresko g & H. Wold (Eds.), Systems under indirect observation :

Causality , structure , pr ediction (Part I). Amsterdam: North-Holland,

183-195.

Sörbom, D. & Jöreskog , K.G. (1976) COFAMM: Con f irmatory f actor anaLysis

with modeL modification . User's guide . Chicago, Illinois: National

Educational Resources .

Sörbom, D. & Jöreskog , K.G. (1981) The use of structural equation models

in evaluation research . Research ReRor t 81 -6, University of Uppsala,

Department of Statistics.

Stevens, J . (1979) Comment on Olson: Choosing a test statistic Ln multivariate

221

analysis of variance. Psychological Bulletin , 86 , 355- 360.

Sti gler, S.M . (197 3) Simon Newcomb, Percy Daniell, and the history of

robust estima tion, 1885-1920 . Journalof the American Statistica l

Association , 68 , 872-879.

Sti gler, S.M . (1980) Studies in the history of probability and sta tistics

XXXVIII . R. H. Smith, A Vic torian int er es t ed in robustnes s . Biometrika ,

67 , 217-221.

Ten Berge, J . M. F . (197 2) Difficulty f ac tors, distrib ution e ffec t s , and

the l east squares s implex da t a matrix solution. Educational and

Psychological Measurement , 32 , 911-920.

Tijmstra, Tj. (1980) Sociologie en tandheelkunde . Resultaten van een gecombi­

neerd sociaal-wetenschappelijk en tandheeZkundig onderzoek . Gron i ngen :

Wolters - Noordhof f . (doc toral dissertati on)

Timm, N. H. (1970) The estimation of variance-covariance and corre l a tion

matrices from incomplete data . Psychometrika , 35 , 417-4 37.

Tukey , J . W. (1977) . ExpZoratory data anaZysis . Reading, Mass achuse tt s :

Addison-Wes l ey .

Van der Sluis, D.M. (1981) St a tistica l progr ams and missing da t a .

Kwantitatieve Methoden , 2 (2), 56-65.

Van Drie l, O. P. (1978) On various cause s of improper solutions in max imum

likelihood factor analysis . Psychometrika , 43 , 225-243 .

Verbeek, A. (1979) Ontbrekende scores bij het schatten van covariantie­

mat rices. VVS BuZZetin , 12 (3), 38-47.

Verdooren, L.R. (1980) On estimation of variance components. Statistica

NeerZandica , 34 , 83-106 .

Vijn , P. (1980) Prior information in linear modeZs . Groningen . (unpublished

doctoral dissertation)

Vijn, P . & Molenaar, I .W. (1981) Robustness regions for dichotomous

decisions. JournaZ of Educational Statistics , 6, 205-235 .

Wainer, H. (1982) Robust statistics: A survey and some prescriptions . In

G. Keren (Ed.), StatisticaZ and methodologicaZ issues in psychoZogy

and sociaZ sciences research . Hillsdale, New Jersey: Erlbaum, 187-

214 .

Wainer, H. & Wright, B.D . (1980) Robust estima tion of abi l ity in the Ras ch

model. Psychometrika , 45 , 373-391.

Wang , p.e.e. (Ed.) (1978) GraphicaZ representation of multivariate data .

New York : Academic Pres s .

Weeks, D. G. (1978) StructuraZ equation systems on latent variabZes within

222

a second- order measurement model . Los Angeles , California: University

of California . (unpublished doctoral dissertation)

Weeks , D.G. (1980) A second-order longitudinal model of ability structure .

Multivar iate Behavioral Research , 15 , 353- 365 .

Werts , C.E., Linn, R.L. & Jöreskog, K.G. (1977) A simplex model for

analyzing academie growth. Educational and Psychological Measurement ,

37 , 745-756.

Werts , C.E., Linn, R.L. & Jöreskog , K. G. (1978) Rel i ab i lity of college

grades from longitudinal data. Educational and Psychological

Measurement , 38 , 89- 95 .

Wheaton , B., Muthén, B., Alwin, D.F. & Surnmers, G. F . (1977) Assessing

reliability and stability in panel models . In D.R. Heise (Ed.),

Sociological methodology 1977. San Francisco : Jossey-Bass, 84-136.

Wiley, D.E. (1973) The identification problem for structural equation

models with unmeasured variables . In A.S. Goldberger & D.D. Duncan

(Eds .), Structural equation models in the social sciences . New York:

~eminar Press , 69-83.

Wiley , D.E., Schmidt , W.H. & Bramble, W.J. (1973) Studies of a class of

covariance structure models. Journalof the American Statis t ica l

Associ ati on , 68 , 317-323 .

Wilk, M.B. & Gnanadesikan, R. (1968) Probability plotting methods for

the analysis of data. Biometrika, 55, 1-17.

Wilks, S.S. (1962) Mathematical s tatis t ics . New York: Wiley.

Wold, H. (1978) Ways and means of multidisciplinary studies. In the

search for absolute values in a changing world. Proceedings of

t he Sixth In t ernati onal Conf erence on the Uni t y of the Sciences ,

San Francisco, 1977. New York: The International Cultural Foundation,

1071-1095.

Wold, H. (1980) Model construction and eva luation when theoretical knowledge

is scarce. Theory and application of partial least squares. In J.

Kmenta & J.B. Ramsey (Eds.), Evaluation of econometrie mode l s. New

York: Academic Press, 47-74.

Wold, H. (1982) Soft modeling: The basic design and some extensions. In

K.G.JÖreskog & H. Wold (Eds.) Sys t ems under indirect observation :

Causali ty , structur e , pr ediction (Part 11). Amsterdam: North-Holland,

1-54.

223