| score_log_nonparam {CommKern} | R Documentation |
Nonparametric score function for distance-based kernel and binary outcome
Description
Description of the nonparametric score function for distance-based kernel function and a binary outcome.
Usage
score_log_nonparam(outcome, dist_mat, grid_gran = 5000)
Arguments
outcome |
a numeric vector containing the binary outcome variable, 0/1 (in the same ID order as dist_mat) |
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 nonparametric kernel test
of association between the kernel and binary 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} = h\left(z_{i}\right) + e_{i},
where
h\left(\cdot\right)
is
the kernel function, z_{i} is a multidimensional array of variables, and y_{i} is a binary outcome taking values in
0, 1.
The function returns an numeric p-value for the kernel score test of association.
Value
the score function p-value
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_cont_nonparam for nonparametric score function of distance-based kernel function and continuous outcome.
score_cont_semiparam for semiparametric 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)
score_log_nonparam(
outcome = simasd_covars$dx_group,
dist_mat = hamil_matrix,
grid_gran = 5000
)