Description Usage Arguments Details Value Author(s) See Also

`fit.simml`

is the workhorse function for Single-index models with multiple-links (SIMML).
The function estimates a linear combination (a single-index) of covariates X, and models the treatment-specific outcome y, via treatment-specific nonparametrically-defined link functions.

1 2 3 4 5 6 7 8 | ```
fit.simml(y, A, X, Xm = NULL, aug = NULL, rho = 0,
family = "gaussian", R = NULL, bs = "ps", k = 8, sp = NULL,
linear.link = FALSE, method = "GCV.Cp", gamma = 1, max.iter = 20,
eps.iter = 0.01, trace.iter = TRUE, ind.to.be.positive = NULL,
scale.si.01 = FALSE, lambda = 0, pen.order = 0, scale.X = TRUE,
center.X = TRUE, ortho.constr = TRUE, beta.ini = NULL,
si.main.effect = FALSE, random.effect = FALSE, z = NULL,
plots = FALSE)
``` |

`y` |
a n-by-1 vector of treatment outcomes; y is a member of the exponential family; any distribution supported by |

`A` |
a n-by-1 vector of treatment variable; each element is assumed to take a value on a continuum. |

`X` |
a n-by-p matrix of baseline covarates. |

`Xm` |
a n-by-q design matrix associated with an X main effect model; the defult is |

`aug` |
a n-by-1 additional augmentation vector associated with the X main effect; the default is |

`rho` |
a tuning parameter associated with the additional augmentation vector |

`family` |
specifies the distribution of y; e.g., "gaussian", "binomial", "poisson"; can be any family supported by |

`R` |
the number of response categories for the case of family = "ordinal". |

`bs` |
basis type for the treatment (A) and single-index domains, respectively; the defult is "ps" (p-splines); any basis supported by |

`k` |
basis dimension for the treatment (A) and single-index domains, respectively. |

`sp` |
smoothing paramter for the treatment-specific link functions; if |

`linear.link` |
if |

`method` |
the smoothing parameter estimation method; "GCV.Cp" to use GCV for unknown scale parameter and Mallows' Cp/UBRE/AIC for known scale; any method supported by |

`gamma` |
increase this beyond 1 to produce smoother models. |

`max.iter` |
an integer specifying the maximum number of iterations for |

`eps.iter` |
a value specifying the convergence criterion of algorithm. |

`trace.iter` |
if |

`ind.to.be.positive` |
for identifiability of the solution |

`scale.si.01` |
if |

`lambda` |
a regularization parameter associated with the penalized LS for |

`pen.order` |
0 indicates the ridge penalty; 1 indicates the 1st difference penalty; 2 indicates the 2nd difference penalty, used in a penalized least squares (LS) estimation of |

`scale.X` |
if |

`center.X` |
if |

`ortho.constr` |
separates the interaction effects from the main effect (without this, the interaction effect can be confounded by the main effect; the default is |

`beta.ini` |
an initial value for |

`si.main.effect` |
if |

`random.effect` |
if |

`z` |
a factor that specifies the random intercepts when |

`plots` |
if |

SIMML captures the effect of covariates via a single-index and their interaction with the treatment via nonparametric link functions.
Interaction effects are determined by distinct shapes of the link functions.
The estimated single-index is useful for comparing differential treatment efficacy.
The resulting `simml`

object can be used to estimate an optimal treatment decision rule
for a new patient with pretreatment clinical information.

a list of information of the fitted SIMML including

`beta.coef` |
the estimated single-index coefficients. |

`g.fit` |
a |

`beta.ini` |
the initial value used in the estimation of |

`beta.path` |
solution path of |

`d.beta` |
records the change in |

`scale.X` |
sd of pretreatment covariates X |

`center.X` |
mean of pretreatment covariates X |

`L` |
number of different treatment options |

`p` |
number of pretreatment covariates X |

`n` |
number of subjects |

`boot.ci` |
(1-boot.alpha/2) percentile bootstrap CIs (LB, UB) associated with |

Park, Petkova, Tarpey, Ogden

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