R: Estimation of polygenic model

polygenic_hglm {GenABEL} | R Documentation

## Estimation of polygenic model

### Description

Estimation of polygenic model using a hierarchical generalized linear model (HGLM; Lee and Nelder 1996. `hglm` package; Ronnegard et al. 2010).

### Usage

      polygenic_hglm(formula, kinship.matrix, data,
        family = gaussian(), conv = 1e-06, maxit = 100, ...)

### Arguments

`formula` | Formula describing fixed effects to be used in analysis, e.g. y ~ a + b means that outcome (y) depends on two covariates, a and b. If no covariates used in analysis, skip the right-hand side of the equation.
`kinship.matrix` | Kinship matrix, as provided by e.g. ibs(,weight="freq"), or estimated outside of GenABEL from pedigree data.
`data` | An (optional) object of `gwaa.data-class` or a data frame with outcome and covariates.
`family` | a description of the error distribution and link function to be used in the mean part of the model (see `family` for details of family functions).
`conv` | 'conv' parameter of `hglm` (stricter than default, for great precision, use 1e-8).
`maxit` | 'maxit' parameter of `hglm` (stricter than default).
`...` | other parameters passed to `hglm` call

### Details

The algorithm gives extended quasi-likelihood (EQL) estimates for restricted maximum likelihood (REML) (Ronnegard et al. 2010). Implemented is the inter-connected GLM interpretation of HGLM (Lee and Nelder 2001). Testing on fixed and random effects estimates are directly done using inter-connected GLMs. Testing on dispersion parameters (variance components) can be done by extracting the profile likelihood function value of REML.

### Author(s)

Xia Shen, Yurii Aulchenko

### References

Ronnegard, L, Shen, X and Alam, M (2010). hglm: A Package For Fitting Hierarchical Generalized Linear Models. The R Journal, 2(2), 20-28.

Lee, Y and Nelder JA (2001). Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions. Biometrika, 88(4), 987-1006.

Lee, Y and Nelder JA (1996). Hierarchical Generalized Linear Models. Journal of the Royal Statistical Society. Series B, 58(4), 619-678.

### See Also

`polygenic`, `mmscore`, `grammar`

### Examples

    require(GenABEL.data)
    data(ge03d2ex.clean)
    set.seed(1)
    df <- ge03d2ex.clean[,sample(autosomal(ge03d2ex.clean),1000)]
    gkin <- ibs(df,w="freq")

    # ----- for quantitative traits
    h2ht <- polygenic_hglm(height ~ sex + age, kin = gkin, df)
    # ----- estimate of heritability
    h2ht$esth2
    # ----- other parameters
    h2ht$h2an

    # ----- test the significance of fixed effects
    # ----- (e.g. quantitative trait)
    h2ht <- polygenic_hglm(height ~ sex + age, kin = gkin, df)
    # ----- summary with standard errors and p-values
    summary(h2ht$hglm)
    # ----- output for the fixed effects part
    # ...
    # MEAN MODEL
    # Summary of the fixed effects estimates
    #              Estimate Std. Error t value Pr(>|t|)
    # (Intercept) 169.53525    2.57624  65.807  < 2e-16 ***
    # sex          14.10694    1.41163   9.993  4.8e-15 ***
    # age          -0.15332    0.05208  -2.944  0.00441 **
    # ---
    # Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    # Note: P-values are based on 69 degrees of freedom
    # ...
    # ----- extract fixed effects estimates and standard errors
    h2ht$h2an

    # ----- test the significance of polygenic effect
    nullht <- lm(height ~ sex + age, df)
    l1 <- h2ht$ProfLogLik
    l0 <- as.numeric(logLik(nullht))
    # the likelihood ratio test (LRT) statistic
    (S <- -2*(l0 - l1))
    # 5% right-tailed significance cutoff
    # for 50:50 mixture distribution between point mass 0 and \chi^{2}(1)
    # Self, SG and Liang KY (1987) Journal of the American Statistical Association.
    qchisq(((1 - .05) - .50)/.50, 1)
    # p-value
    pchisq(S, 1, lower.tail = FALSE)/2

    # ----- for binary traits
    h2dm <- polygenic_hglm(dm2 ~ sex + age, kin = gkin, df, family = binomial(link = 'logit'))
    # ----- estimated parameters
    h2dm$h2an

[Package GenABEL version 1.8-0 Index]