Multivariate Normal Model

Author(s):  
Jie Chen ◽  
Arjun K. Gupta
1991 ◽  
Vol 70 (2) ◽  
pp. 770-777 ◽  
Author(s):  
J. L. Hopper ◽  
M. E. Hibbert ◽  
G. T. Macaskill ◽  
P. D. Phelan ◽  
L. I. Landau

Lung function and height in 242 8-yr-old and 299 12-yr-old children without known or suspected predisposition to lung disease were measured annually over 6 and 8 yr, respectively. Growth of forced expiratory volume in 1 s (FEV1), vital capacity, and expiratory flow after expiring 50% of vital capacity were statistically modeled by age and height by use of a multivariate normal model for longitudinal data. This method has the flexibility to fit an appropriate (not necessarily linear) mathematical description of average lung function while concurrently modeling the covariance between measures on the same individual. Differences in lung function growth between girls and boys, pre- and post-puberty, showed that girls had a steadier though less pronounced increase in lung function with height. In boys, before puberty there was deficit in lung volume relative to height (not evident in girls), which was compensated for by rapid growth after puberty. The standard error of FEV1 predictions based on current height and age were more than halved when measurements of FEV1, age, and height taken 1 yr before were incorporated. We found evidence for dysanaptic growth in childhood. Fitted models have application to early detection of departures from healthy lung function.


Genetics ◽  
1990 ◽  
Vol 125 (1) ◽  
pp. 207-213 ◽  
Author(s):  
M Slatkin ◽  
S A Frank

Abstract The independence of two phenotypic characters affected by both pleiotropic and nonpleiotropic mutations is investigated using a generalization of M. Slatkin's stepwise mutation model of 1987. The model is used to determine whether predictions of either the multivariate normal model introduced in 1980 by R. Lande or the house-of-cards model introduced in 1985 by M. Turelli can be regarded as typical of models that are intermediate between them. We found that, under stabilizing selection, the variance of one character at equilibrium may depend on the strength of stabilizing selection on the other character (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the types of mutations that can occur. Similarly, under directional selection, the genetic covariance between two characters may increase substantially (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the kinds of mutations that are assumed to occur. Hence, even for the simple model we consider, neither the house-of-cards nor the multivariate normal model can be used to make predictions, making it unlikely that either could be used to draw general conclusions about more complex and realistic models.


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