# zbMATH — the first resource for mathematics

Repeated measures with zeros. (English) Zbl 1121.62574
Summary: Illinois State University, Normal, USA and PA Lachenbruch FDA Center for Biologics Research and Review, Rockville, MD, USA, kberkatilstu.edu Consider repeated measures data with many zeros. For the case with one grouping factor and one repeated measure, we examine several models, assuming that the nonzero data are roughly lognormal. One of the simplest approaches is to model the zeros as left-censored observations from the lognormal distribution. A random effectis assumed for subjects. The censored model makes a strong assumption about the relationship between the zeros and the nonzero values. To check on this, you can instead assume that some of the zeros are ’true’ zeros and model them as Bernoulli. Then the other values are modeled with a censored lognormal. A logistic model is used for the Bernoulli $$p$$, the probability of a true nonzero. The fit of the pure left-censored lognormal can be assessed by testing the hypothesis that $$p$$ is 1, as described by Moulton and Halsey.$$^{1}$$ The model can also be simplified by omitting the censoring, leaving a logistic model for the zeros and a lognormal model for the nonzero values. This is approximately equivalent to modeling the zero and nonzero values separately, a two-part model. In contrast to the censored model, this model assumes only a slight relationship (a covariance component) between the occurrence of zeros and the size of the nonzero values. The models are compared in terms of an example with data from children’s private speech.
Reviewer: Reviewer (Berlin)

##### MSC:
 62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text:
##### References:
 [1] Moulton LH, Biometrics 51 pp 1570– (1995) · Zbl 0875.62502 · doi:10.2307/2533289 [2] Moulton LH, Vaccine 14 pp 1154– (1996) · doi:10.1016/0264-410X(96)00017-5 [3] Zhou X-H, Biometrics 55 pp 645– (1999) · Zbl 1059.62518 · doi:10.1111/j.0006-341X.1999.00645.x [4] Olsen MK, Journal of the American Statistical Association 96 pp 730– (2001) · Zbl 1017.62064 · doi:10.1198/016214501753168389 [5] Davis, CS., Statistical analysis of medical data: new developments pp 145– (1998) [6] Lachenbruch PA., Biometrische Zeitschrift 18 pp 351– (1976) [7] Tobin, J., Econometrica 26 pp 24– (1958) · Zbl 0088.36607 · doi:10.2307/1907382 [8] Amemiya, T., Journal of Econometrics 24 pp 3– (1984) · Zbl 0539.62121 · doi:10.1016/0304-4076(84)90074-5 [9] Feuerverger A., Biometrika 66 pp 655– (1979) · doi:10.1093/biomet/66.3.655 [10] Bivens JA, Merrill-Palmer Quarterly 36 pp 443– (1990) [11] Self SG, Journal of the American Statistical Association 82 pp 605– (1987) · doi:10.1080/01621459.1987.10478472
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.