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.

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
)



[Package CommKern version 1.0.1 Index]