score_cont_nonparam {CommKern}

Nonparametric score function for distance-based kernel and continuous outcome.

Description

Description of the nonparametric score function for distance-based kernel function and continuous outcome.

Usage

score_cont_nonparam(outcome, dist_mat, grid_gran = 5000)

Arguments

outcome

a numeric vector containing the continuous outcome variable (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 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} = 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 continuous outcome taking values in in the real numbers.

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_log_nonparam for nonparametric score function of distance-based kernel functions and binary 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_cont_nonparam(
  dist_mat = hamil_matrix,
  outcome = simasd_covars$verbal_IQ,
  grid_gran = 5000
)