| score_cont_semiparam {CommKern} | R Documentation |
Semiparametric score function for distance-based kernel and continuous outcome.
Description
Description of the semiparametric score function for distance-based kernel function and continuous outcome.
Usage
score_cont_semiparam(outcome, covars, dist_mat, grid_gran = 5000)
Arguments
outcome |
a numeric vector containing the continuous outcome variable (in the same ID order as dist_mat) |
covars |
a data frame containing the covariates to be modeled parametrically (should NOT include an ID variable) |
dist_mat |
a square distance matrix |
grid_gran |
a numeric value specifying the grid search length, preset to 5000 |
Details
This is the main function that calculates the p-value associated with a semiparametric kernel test
of association between the kernel and continuous outcome variable. A null model (where the kernel is not
associated with the outcome) is initially fit. Then, the variance of
Y_{i}|X_{i} is used as the basis for the
score test,
S\left(\rho\right) = \frac{Q_{\tau}\left(\hat{\beta_0},\rho\right)-\mu_Q}{\sigma_Q}.
However,
because \rho disappears under the null hypothesis, we run a grid search over a range of values of \rho (the bounds
of which were derived by Liu et al. in 2008). This grid search gets the upper bound for the score test's p-value.
This function is tailored for the underlying model
y_{i} = x_{i}^{T}\beta + h\left(z_{i}\right) + e_{i},
where h\left(\cdot\right) is
the kernel function, z_{i} is a multidimensional array of variables, x_{i} is a vector or matrix of covariates, \beta is a vector
of regression coefficients, and y_{i} is a continuous outcome taking values in the real numbers.
Value
the score function p-value for the kernel score test of association.
References
Liu D, Ghosh D, and Lin X (2008) "Estimation and testing for the effect of a genetic pathway on a disease outcome using logistic kernel machine regression via logistic mixed models." BMC Bioinformatics, 9(1), 292. ISSN 1471-2105. doi:10.1186/1471-2105-9-292.
See Also
hms, ext_distance, ham_distance
score_log_semiparam for semiparametric score function of distance-based kernel functions and binary outcome.
score_log_nonparam for nonparametric score function of distance-based kernel functions and binary outcome.
score_cont_nonparam for nonparametric score function of distance-based kernel function and continuous outcome.
Examples
data(simasd_hamil_df)
data(simasd_covars)
hamil_matrix <- ham_distance(simasd_hamil_df)
covars_df <- simasd_covars[,3:4]
score_cont_semiparam(
outcome = simasd_covars$verbal_IQ,
covars = covars_df,
dist_mat = hamil_matrix,
grid_gran = 5000
)