The estimation of variance-covariance and correlation matrices from incomplete data

Timm, Neil H.

doi:10.1007/bf02291818

Cited by 54 publications

(23 citation statements)

References 13 publications

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“…However, when the proportion of incomplete observations is high or when the pattern of the missing entries is highly non-random, it seems plausible that one of the many methods of assigning values to the missing entries should be applied&dquo; (Haitovsky, 1968: 67). Later publications based on simulations do not consider the pairwise deletion partly on the basis of evidence presented by Haitovsky (e.g., Timm, 1970;Beale and Little, 1974).…”

Section: Listwise and Pairwise Deletionmentioning

confidence: 98%

The Treatment of Missing Data in Multivariate Analysis

Kim

Curry

1977

Sociological Methods & Research

224

151

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Procedures for treating missing data in the statistical analysis of survey data are reviewed. The main topics covered are: (1) how to assess the nature of missing data especially with regard to randomness, (2) a comparison of listwise and pairwise deletion, and (3) methods for using maximum information to estimate (a) parameters or (b) missing values. any large data set it is unlikely that complete information or any large data set it is unlikely that complete information will be present for all the cases. In surveys which rely on respondents' reports of behavior and attitudes, it is almost certain that some information is either missing or in an unusable form. Although statisticians have long appreciated that the existence of such missing information can change an ordinarily simple statistical analysis into a complex one (e.g., Orchard and Woodbury, 1972) and responded to this challenge by producing enormous amounts of literature (see, for example, Afifi and Elashoff, 1966;Hartley and Hocking, 1971;Orchard and Woodbury, 1972;Press and Scott, 1974), there is little indication that survey researchers have paid much attention to the literature. When faced with such missing-data problems, most survey researchers are likely to choose either a listwise deletion or pairwise deletion, and then proceed to interpret the resulting statistics as usual. 1 The primary objective of this paper is to review and organize the procedures for handling missing data, having in mind the practical needs of survey researchers with a relatively complex analysis problem but with little statistical sophistication. To make the task manageable, we will confine our discussion mostly to the situation in which variables are measured at least on an interval scale. Other situations will be dealt with only when such excursion is simple and does not interrupt the flow of the presentation. For researchers with specific problems not discussed in this paper, a brief bibliographical note is included.

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Section: Listwise and Pairwise Deletionmentioning

confidence: 98%

The Treatment of Missing Data in Multivariate Analysis

Kim

Curry

1977

Sociological Methods & Research

224

151

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“…When the number of measurements made on each individual is large, such incomplete observations may become an important problem. Various ways of handling missing values have been extensively studied from the standpoint of the estimation of population parameters in multivariate analysis [5,16,18,19,20,23,24,26] and in regression analysis [io, 12,14,15,21,25]. The effects of these methods on the probability of correct classification in discriminant analysis have, however, not been extensively studied.…”

Section: Introductionmentioning

confidence: 99%

The Treatment of Missing Values in Discriminant Analysis—I. The Sampling Experiment

Chan

Dunn

1972

Journal of the American Statistical Association

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2.1) (2.3) Probabilitie. of correct cla..ificafion under several commonly u.ed method. of handling mi.sing value. are .tudied by Monte Carlo method•. The method. include u'e of only complete observation vectors; u'e of all observation. with no replacement; .ub.titution of mean. for missing ob.ervations; Buck's regression method; and, Dear'. principal component method. Discriminant functions were formed u.ing independent random sample. from two multivariate normal distribution. with equal covariance matrices. Mis.ing values occur randomly in each variable and independently of mi..ing value. in other variable•. The mean .ubstitution method and principal component method are, in general, .uperior to the other methods for ca.e. considered.

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“…Some authors base imputations on a principal component analysis (Dear 1959;Timm 1970). But a more obvious (and in my view, more promising) approach is to impute for a missing X by linear regression on the observed X's in that case, estimated from the complete cases (Dagenais 1973).…”

Section: Conditional Mean Imputation Based On X'smentioning

confidence: 99%

Regression With Missing X's: A Review

Little¹

1992

Journal of the American Statistical Association

701

735

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Statistical Association.http://www.jstor.org Regression With Missing X's: A Review RODERICK J. A. LITTLE* The literature of regression analysis with missing values of the independent variables is reviewed. Six classes of procedures are distinguished: complete case analysis, available case methods, least squares on imputed data, maximum likelihood, Bayesian methods, and multiple imputation. Methods are compared and illustrated when missing data are confined to one independent variable, and extensions to more general patterns are indicated. Attention is paid to the performance of methods when the missing data are not missing completely at random. Least squares methods that fill in missing X's using only data on the X's are contrasted with likelihoodbased methods that use data on the X's and Y. The latter approach is preferred and provides methods for elaboration of the basic normal linear regression model. It is suggested that more widely distributed software is needed that advances beyond complete-case analysis, available-case analysis, and naive imputation methods. Bayesian simulation methods and multiple imputation are reviewed; these provide fruitful avenues for future research.

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The estimation of variance-covariance and correlation matrices from incomplete data

Cited by 54 publications

References 13 publications

The Treatment of Missing Data in Multivariate Analysis

The Treatment of Missing Data in Multivariate Analysis

The Treatment of Missing Values in Discriminant Analysis—I. The Sampling Experiment

Regression With Missing X's: A Review

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