pathmix {pathmix} | R Documentation |
This package implements the path models for quantitative phenotypes such as blood pressure as described in Morton et al. (1983). The raw data are condensed into estimates of familial correlations and then analysed according to models parametrised for nuclear families and fitted by the maximum likelihood estimates (MLEs).
Let r_i, i=1,...,m denote m observed correlations with corresponding sample sizes n_i. Let z_i denote Fisher's z-transformation of r_i=1/2ln[(1+r_i)/(1-r_i)]. If the covariance matrix between the z values is denoted by Σ, the log-likelihood of the observed data can be written, assuming multivariate normality for all the z valuess, as
ln L = - X^2/2 + constant
where
X^2 = (z - zbar)' Sigma^(-1)(z-zbar)
ignoring the bias term which has a negligibale effect on the results. Here z is a column vector of the observed z-transforms, and zbar a column vector of z-transforms of the expected correlations rho_i which are derived as functions of path coefficients under a given model. In the likelihood function, a power of the determinant |Sigma| was incorporated into the `constant', emipirically it is found that this quantity hardly changes for different models. Likelihood ratio tests (LRTs) can be carried out between nested models containing different number of parameters according to the standard asymptotic theory.
Specification of the covariance matrix Σ depends on how the data are obtained. If z_i are indepedent (estimated from different samples), covariance between z_i and z_j is zero (i<>j). Then it is known that asymptotic properties hold good even for small to moderate sample sizes and the X^2 expression simplies to
X^2 = sum_i (z_i - zbar)^2
by taking the variance of z_i as 1/n_i ignoring refinements.
It is possible to perform heterogeneity testing among multiple studies under models described above.
The path diagram (.pdf) together with the graphviz diagram (.dot) are given in doc directory of the installed package and inst/doc of the source package.
The path model assumes that family environment (C), or the transmissible environment, acts additively with genotype (G) to produce a phenotype (P), all interactions being negligible. Environmental indicies (I) are created and treated as correlated phenotypes. Furthermore, the model allows for assortative mating through a copath (p) and social homogamy (H) is treated in terms of simple paths (m, u) lying in the interval [-1,1]. Specific maternal effects are included by distinguishing f_F and f_M the effects of parents' environments on that of a child reared by them, with F and M denoting father and mother respectively. Intergenerational differences in genetic and environmental effects are retained such that the genetic and environmental (cultural) heritabilities in children are h^2 and c^2 respectively, and h^2z^2 and c^2y^2 in adults. A non-transmitted sibship environment (B) is incorporated such that the correlation between sibling environments due to non-transmitted environment is b^2 in young sibs, and b^2x^2 in adult sibs. Similarly, the path coefficients associated with environmental indices are i and iv respectively for young children and adults, those of genotype to indices j and jw for young children and adults. The path coefficients from parents' genotypes to children are assumed 1/2 ignoring age effect. The correlation between an individual's adulthood and childhood genotype is represented by r_G.
Further details concerning the expected correlations, nonlinear constraints (which differentiate the need of optimisation routine ALMINI rather than GEMINI) can be found in Morton et al. (1983).
pathmix(iop=3, datfile="data", jobfile="job", profile="prolix", terfile="summary")
iop |
iop=1,2,3,4 for ALMINI test, GEMINI test, path3a, path3b | ||||||||||
datfile |
The data file | ||||||||||
jobfile |
The job file. The original skeleton is given as follows,
PX(1)(ID=1, PO=2, PH=4, IN=3) FM(27)(18X, F3.0, 2X, A1, 2X, 2F8.4) TR(9)(4)(4)(0.,1.) CC comments EOF XY(ALL) PA(R11=R12=0.938) IT(R11=R12)(h=0.01,T=0.001) EOF PA(H=0.85,...) IT(H,C)(H=0.001,T=0.0001,INLC=0) IT(...) PA(...) IT(...) EOF DATA=TONG SUMMARY=WW1 PROLIX=WW2 EOF inidividual correlations EOF Pooled observed correlations EOF EOT The six files (marked by EOF) were required by PATHMIX for the following information:
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profile |
The prolix file | ||||||||||
terfile |
The terse or summary file |
At the moment, no value is returned and the outputs is read through the file.show function.
Morton N.E., Rao D.C & Lalouel J-M (1983). Methods in Genetic Epidemiology. Karger PO Box, CH-4009 Basel (Switzerland).
The software documentation is given in the inst/doc (source package) or doc (the installed package) directory.
## Not run: # test for ALMINI, check files ALMTEST.OUT and ALMTEST.PLX pathmix(1) # test for GEMINI, check files GEMTEST.OUT and GEMTEST.PLX pathmix(2) # path3a pathmix(3, datfile="TEST.DAT", jobfile="test.jf") # path3b pathmix(4, datfile="TEST.DAT", jobfile="test.jf") ## End(Not run)