Description Usage Arguments Details Value WARNINGS Author(s) References See Also Examples

`SemiParTRIV`

fits flexible trivariate binary models with several types of covariate effects.

1 2 3 4 5 6 7 | ```
SemiParTRIV(formula, data = list(), weights = NULL, subset = NULL,
Model = "T", margins = c("probit", "probit", "probit"),
penCor = "unpen", sp.penCor = 3,
approx = FALSE, Chol = FALSE, infl.fac = 1,
gamma = 1, w.alasso = NULL, rinit = 1, rmax = 100,
iterlimsp = 50, tolsp = 1e-07,
gc.l = FALSE, parscale, extra.regI = "t")
``` |

`formula` |
In the basic setup this will be a list of three formulas. |

`data` |
An optional data frame, list or environment containing the variables in the model. If not found in |

`weights` |
Optional vector of prior weights to be used in fitting. |

`subset` |
Optional vector specifying a subset of observations to be used in the fitting process. |

`Model` |
It indicates the type of model to be used in the analysis. Possible values are "T" (trivariate model), "TSS" (trivariate model with double sample selection). |

`margins` |
It indicates the link functions used for the three margins. Possible choices are "probit", "logit", "cloglog"". |

`penCor` |
Type of penalty for correlation coefficients. Possible values are "unpen", "lasso", "ridge", "alasso". |

`sp.penCor` |
Starting value for smoothing parameter of |

`approx` |
If |

`Chol` |
If |

`infl.fac` |
Inflation factor for the model degrees of freedom in the approximate AIC. Smoother models can be obtained setting this parameter to a value greater than 1. |

`gamma` |
Inflation factor used only for the alasso penalty. |

`w.alasso` |
When using the alasso penalty a weight vector made up of three values must be provided. |

`rinit` |
Starting trust region radius. The trust region radius is adjusted as the algorithm proceeds. See the documentation
of |

`rmax` |
Maximum allowed trust region radius. This may be set very large. If set small, the algorithm traces a steepest descent path. |

`iterlimsp` |
A positive integer specifying the maximum number of loops to be performed before the smoothing parameter estimation step is terminated. |

`tolsp` |
Tolerance to use in judging convergence of the algorithm when automatic smoothing parameter estimation is used. |

`gc.l` |
This is relevant when working with big datasets. If |

`parscale` |
The algorithm will operate as if optimizing objfun(x / parscale, ...) where parscale is a scalar. If missing then no
rescaling is done. See the
documentation of |

`extra.regI` |
If "t" then regularization as from |

This function fits trivariate binary models.

For sample selection models, if there are factors in the model, before fitting, the user has to ensure
that the numbers of factor variables' levels in the selected sample
are the same as those in the complete dataset. Even if a model could be fitted in such a situation,
the model may produce fits which are
not coherent with the nature of the correction sought. For more details see `?SemiParBIV`

.

The function returns an object of class `SemiParTRIV`

as described in `SemiParTRIVObject`

.

Convergence can be checked using `conv.check`

which provides some
information about
the score and information matrix associated with the fitted model. The former should be close to 0 and the latter positive definite.
`SemiParTRIV()`

will produce some warnings if there is a convergence issue.

Convergence failure may sometimes occur. This is not necessarily a bad thing as it may indicate specific problems
with a fitted model. In such a situation, the user may use some extra regularisation (see `extra.regI`

) and/or
rescaling (see `parscale`

). Penalising the correlations using argument `penCor`

may help a lot as
in our experience in hard situations the correlation coefficients are typically the most difficult to estimate.
The user should also consider re-specifying/simplifying the model. Moreover, when using
smooth functions, if the covariate's values are too sparse then convergence may be affected by this. It is also helpful to
look into the proportions of 1 and 0 available for each event of the trivariate model; it may
be the case that certain events do not have many observations associated with them, in which case estimation may be more challenging.

Authors: Panagiota Filippou, Giampiero Marra and Rosalba Radice

Maintainer: Giampiero Marra [email protected]

Filippou P., Marra G. and Radice R. (in press), Penalized Likelihood Estimation of a Trivariate Additive Probit Model. *Biostatistics*.

`SemiParBIV`

, `copulaReg`

, `copulaSampleSel`

, `JRM-package`

, `SemiParTRIVObject`

, `conv.check`

, `summary.SemiParTRIV`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 | ```
## Not run:
library(JRM)
############
## EXAMPLE 1
############
## Generate data
## Correlation between the two equations 0.5 - Sample size 400
set.seed(0)
n <- 400
Sigma <- matrix(0.5, 3, 3); diag(Sigma) <- 1
u <- rMVN(n, rep(0,3), Sigma)
x1 <- round(runif(n)); x2 <- runif(n); x3 <- runif(n)
f1 <- function(x) cos(pi*2*x) + sin(pi*x)
f2 <- function(x) x+exp(-30*(x-0.5)^2)
y1 <- ifelse(-1.55 + 2*x1 - f1(x2) + u[,1] > 0, 1, 0)
y2 <- ifelse(-0.25 - 1.25*x1 + f2(x2) + u[,2] > 0, 1, 0)
y3 <- ifelse(-0.75 + 0.25*x1 + u[,3] > 0, 1, 0)
dataSim <- data.frame(y1, y2, y3, x1, x2)
f.l <- list(y1 ~ x1 + s(x2),
y2 ~ x1 + s(x2),
y3 ~ x1)
out <- SemiParTRIV(f.l, data = dataSim)
out1 <- SemiParTRIV(f.l, data = dataSim, Chol = TRUE)
conv.check(out)
summary(out)
plot(out, eq = 1)
plot(out, eq = 2)
AIC(out)
BIC(out)
out <- SemiParTRIV(f.l, data = dataSim,
margins = c("probit","logit","cloglog"))
out1 <- SemiParTRIV(f.l, data = dataSim, Chol = TRUE,
margins = c("probit","logit","cloglog"))
conv.check(out)
summary(out)
plot(out, eq = 1)
plot(out, eq = 2)
AIC(out)
BIC(out)
f.l <- list(y1 ~ x1 + s(x2),
y2 ~ x1 + s(x2),
y3 ~ x1,
~ 1, ~ 1, ~ 1)
out1 <- SemiParTRIV(f.l, data = dataSim, Chol = TRUE)
f.l <- list(y1 ~ x1 + s(x2),
y2 ~ x1 + s(x2),
y3 ~ x1,
~ 1, ~ s(x2), ~ 1)
out2 <- SemiParTRIV(f.l, data = dataSim, Chol = TRUE)
f.l <- list(y1 ~ x1 + s(x2),
y2 ~ x1 + s(x2),
y3 ~ x1,
~ x1, ~ s(x2), ~ x1 + s(x2))
out2 <- SemiParTRIV(f.l, data = dataSim, Chol = TRUE)
f.l <- list(y1 ~ x1 + s(x2),
y2 ~ x1 + s(x2),
y3 ~ x1,
~ x1, ~ x1, ~ s(x2))
out2 <- SemiParTRIV(f.l, data = dataSim, Chol = TRUE)
f.l <- list(y1 ~ x1 + s(x2),
y2 ~ x1 + s(x2),
y3 ~ x1,
~ x1, ~ x1 + x2, ~ s(x2))
out2 <- SemiParTRIV(f.l, data = dataSim, Chol = TRUE)
f.l <- list(y1 ~ x1 + s(x2),
y2 ~ x1 + s(x2),
y3 ~ x1,
~ x1 + x2, ~ x1 + x2, ~ x1 + x2)
out2 <- SemiParTRIV(f.l, data = dataSim, Chol = TRUE)
############
## EXAMPLE 2
############
## Generate data
## with double sample selection
set.seed(0)
n <- 5000
Sigma <- matrix(c(1, 0.5, 0.4,
0.5, 1, 0.6,
0.4, 0.6, 1 ), 3, 3)
u <- rMVN(n, rep(0,3), Sigma)
f1 <- function(x) cos(pi*2*x) + sin(pi*x)
f2 <- function(x) x+exp(-30*(x-0.5)^2)
x1 <- runif(n)
x2 <- runif(n)
x3 <- runif(n)
x4 <- runif(n)
y1 <- 1 + 1.5*x1 - x2 + 0.8*x3 - f1(x4) + u[, 1] > 0
y2 <- 1 - 2.5*x1 + 1.2*x2 + x3 + u[, 2] > 0
y3 <- 1.58 + 1.5*x1 - f2(x2) + u[, 3] > 0
dataSim <- data.frame(y1, y2, y3, x1, x2, x3, x4)
f.l <- list(y1 ~ x1 + x2 + x3 + s(x4),
y2 ~ x1 + x2 + x3,
y3 ~ x1 + s(x2))
out <- SemiParTRIV(f.l, data = dataSim, Model = "TSS")
conv.check(out)
summary(out)
plot(out, eq = 1)
plot(out, eq = 3)
prev(out)
prev(out, type = "univariate")
prev(out, type = "naive")
## End(Not run)
``` |

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