BoostMLR {BoostMLR} | R Documentation |

Function jointly models the multiple longitudinal responses (referred to as multivariate longitudinal response) and multiple covariates and time from a longitudinal study using gradient boosting approach (Pande et al., 2020). Covariates can be time-varying or time-invariant. Special cases include modeling of univariate longitudinal response from a longitudinal study, and univariate or multivariate response from a cross-sectional study. In all cases, responses are assumed to be continuous. The estimated coefficient can be a function of time (referred to as time-varying coefficient in case of a longitudinal study) or a function of pre-specified covariate (in case of a longitudinal or a cross-sectional study) or fixed.

```
BoostMLR(x,
tm,
id,
y,
Time_Varying = TRUE,
BS_Time = TRUE,
nknots_t = 10,
d_t = 3,
All_RawX = TRUE,
RawX_Names,
nknots_x = 7,
d_x = 3,
M = 200,
nu = 0.05,
Mod_Grad = TRUE,
Shrink = FALSE,
VarFlag = TRUE,
lower_perc = 0.25,
upper_perc = 0.75,
NLambda = 100,
Verbose = TRUE,
Trace = FALSE,
lambda = 0,
setting_seed = FALSE,
seed_value = 100L,
...)
```

`x` |
Data frame (or matrix) containing x-values (covariates).
The number of rows should match with number of rows of response |

`tm` |
Vector of time values, one entry for each row of the response |

`id` |
Vector of subject identifier with same length as the number of rows of |

`y` |
Data frame (or matrix) containing the y-values (response) in case of multivariate response or a vector of y-values in case of univariate response. |

`Time_Varying` |
Time-varying coefficient model or a fixed coefficient model? |

`BS_Time` |
If |

`nknots_t` |
If |

`d_t` |
If |

`All_RawX` |
Use original scale of |

`RawX_Names` |
If |

`nknots_x` |
Specify number of knots for B-spline of |

`d_x` |
Specify degree of polynomial for B-spline of |

`M` |
Number of boosting iterations. |

`nu` |
Boosting regularization parameter. A value from the interval (0,1]. |

`Mod_Grad` |
Use a modified gradient? Modified gradient is a special type of gradient that is independent of the correlation coefficient. Pande A. (2017) observed that prediction performance increases under modified gradient. |

`Shrink` |
Allow estimated coefficient to shrink to zero using L1 penalization? |

`VarFlag` |
Estimate the variance (scale parameter) and correlation parameter
for each |

`lower_perc` |
Lower percentile value is used to determine the lower cut-off for the distribution of parameter estimate. Applicable when |

`upper_perc` |
Upper percentile value is used to determine the upper cut-off for the distribution of parameter estimate. Applicable when |

`NLambda` |
Number of replications for generating distribution of parameter estimates. Applicable when |

`Verbose` |
Print the current stage of boosting iteration? |

`Trace` |
Print the current stage of execution? Useful for identifying location in case error occurs. |

`lambda` |
Additional penaulty; not implemented at this time. |

`setting_seed` |
Set |

`seed_value` |
Seed value. |

`...` |
Further arguments passed to or from other methods. |

This is a non-parametric approach for joint modeling of a multivariate longitudinal response, which is based on marginal model. Estimation is performed using gradient boosting, a generic form of boosting (Friedman J. H., 2001). Our boosting approach is closely related to component-wise L2 boosting with L1 penalization. Approach can handle high dimensionalilty of covariate and response when some of the covariates and responses are pure noise.

Approach is designed to identify covariates that affect responses differently as different time intervals. This idea is helpful to dissect an overall effect of covariate into different time intervals. For example, some covariates affect response at the beginning of the follow-up whereas others at a later stage.

Shrinking allows for early termination of boosting to prevent overfitting. Also, it provides a parsimonious model by shrinking coefficient for non-informative covariate-response pair to zero.

`x` |
Matrix containing x-values. |

`id` |
Vector of subject identifier. |

`tm` |
Vector of time values. |

`y` |
Matrix containing y-values. |

`UseRaw` |
Logical vector indicating indexes of covariates which are used as it is without B-spline mapping. |

`x_Names` |
Variable names of |

`y_Names` |
Variable names of |

`M` |
Number of boosting iterations. If boosting terminates before
a pre-specified |

`nu` |
Regularization parameter. |

`Tm_Beta` |
An estimate of the parameter beta. This consist of a list of
length equal to the number of multivariate response (denoted by L). If |

`mu` |
Estimate of the conditional expectation of |

`Error_Rate` |
Training error rate for each response across the boosting iterations. |

`Variable_Select` |
Indexes of important covariates that get picked-up across time and across boosting iterations. Result is shown as a matrix with M rows and H (number of overlapping time intervals) columns, where each element represents index of covariate. |

`Response_Select` |
Indexes of important responses that get picked-up across time and across boosting iterations. Result is shown as a matrix with M rows and H columns, where each element represents index of response variable. |

`VarFlag` |
Whether the variance (scale parameter) and correlation are estimated? |

`Time_Varying` |
Whether estimates are time-varying or fixed? |

`Phi` |
Matrix, having dimension M by L, representing an estimate of variance (scale parameter) for each response across the boosting iterations. |

`Rho` |
Matrix, having dimension M by L, represent an estimate of correlation for each response across the boosting iterations. |

`Lambda_List` |
Estimate of the lambda (the L1 penaulty parameter) for each boosting iterations. Useful for internal calculation. |

`Grow_Object` |
Useful for internal calculation. |

Amol Pande and Hemant Ishwaran

Pande A., Ishwaran H., Blackstone E.H. (2020). Boosting for multivariate longitudinal response.

Pande A., Li L., Rajeswaran J., Ehrlinger J., Kogalur U.B.,
Blackstone E.H., Ishwaran H. (2017). Boosted multivariate trees for
longitudinal data, *Machine Learning*, 106(2): 277–305.

Pande A. (2017). *Boosting for longitudinal data*. Ph.D. Dissertation,
Miller School of Medicine, University of Miami.

Friedman J.H. (2001). Greedy function approximation: a gradient
boosting machine, *Ann. of Statist.*, 5:1189-1232.

`updateBoostMLR`

,
`predictBoostMLR`

,
`simLong`

```
##-----------------------------------------------------------------
## Multivariate Longitudinal Response
##-----------------------------------------------------------------
# Simulate data involves 3 response and 4 covariates
dta <- simLong(n = 100, N = 5, rho =.80, model = 1, q_x = 0,
q_y = 0,type = "corCompSym")$dtaL
# Boosting call: Raw values of covariates, B-spline for time,
# no shrinkage, no estimate of rho and phi
boost.grow <- BoostMLR(x = dta$features, tm = dta$time, id = dta$id,
y = dta$y, M = 100, VarFlag = FALSE)
# Plot training error
plotBoostMLR(boost.grow$Error_Rate,xlab = "m",ylab = "Training Error")
##-----------------------------------------------------------------
## Laboratory data
##-----------------------------------------------------------------
data(Laboratory_Data, package = "BoostMLR")
Var_Names <- colnames(Laboratory_Data)
x_Names <- setdiff(Var_Names, c("id","time","tbili_po","creat_po"))
dta_id <- Laboratory_Data[,"id"]
dta_time <- Laboratory_Data[,"time"]
dta_x <- Laboratory_Data[,x_Names]
dta_y <- Laboratory_Data[,c("tbili_po","creat_po")]
boost.grow <- BoostMLR(x = dta_x,tm = dta_time,id = dta_id,y = dta_y,
Time_Varying = TRUE,BS_Time = TRUE,
All_RawX = TRUE,M = 10, VarFlag = TRUE)
##-----------------------------------------------------------------
## Univariate Longitudinal Response
##-----------------------------------------------------------------
# Simulate data involves 1 response and 4 covariates
dta <- simLong(n = 100, N = 5, rho =.80, model = 2, q_x = 0,
q_y = 0,type = "corCompSym")$dtaL
# Boosting call: B-spline for time and covariates, shrinkage,
# estimate of rho and phi
boost.grow <- BoostMLR(x = dta$features, tm = dta$time, id = dta$id,
y = dta$y, M = 100, BS_Time = TRUE,
All_RawX = FALSE, Shrink = TRUE,VarFlag = TRUE)
# Plot training error
plotBoostMLR(boost.grow$Error_Rate,xlab = "m",ylab = "Training Error")
# Plot phi
plotBoostMLR(boost.grow$Phi,xlab = "m",ylab = "phi")
# Plot rho
plotBoostMLR(boost.grow$Rho,xlab = "m",ylab = "rho")
##-----------------------------------------------------------------
## Multivariate Longitudinal Response
##-----------------------------------------------------------------
# Simulate data involves 3 response and 4 covariates
dta <- simLong(n = 100, N = 5, rho =.80, model = 1, q_x = 0,
q_y = 0,type = "corCompSym")$dtaL
# Boosting call: Raw values of covariates, fixed parameter estimates
# instead of time varying, no shrinkage, no estimate of rho and phi
boost.grow <- BoostMLR(x = dta$features, tm = dta$time, id = dta$id,
y = dta$y, M = 100,Time_Varying = FALSE,VarFlag = FALSE)
# Print parameter estimates
boost.grow$Tm_Beta
##-----------------------------------------------------------------
## Multivariate Response from Cross-sectional Data: Estimated
## coefficient as a function of covariate
##-----------------------------------------------------------------
if (library("mlbench", logical.return = TRUE)) {
data("BostonHousing")
x <- BostonHousing[,c(1:7,9:12)]
tm <- BostonHousing[,8]
id <- 1:nrow(BostonHousing)
y <- BostonHousing[,13:14]
# Boosting call: Raw values of covariates, B-spline for covariate "dis",
# no shrinkage
boost.grow <- BoostMLR(x = x, tm = tm, id = id, y = y, M = 100,VarFlag = FALSE)
# Plot training error
plotBoostMLR(boost.grow$Error_Rate,xlab = "m",ylab = "Training Error",
legend_fraction_x = 0.2)
}
##-----------------------------------------------------------------
## Univariate Response from Cross-sectional Data: Fixed estimated
## coefficient
##-----------------------------------------------------------------
if (library("mlbench", logical.return = TRUE)) {
library(mlbench)
data("BostonHousing")
x <- BostonHousing[,1:13]
y <- BostonHousing[,14]
# Boosting call: Raw values of covariates
boost.grow <- BoostMLR(x = x, y = y, M = 100)
# Plot training error
plotBoostMLR(boost.grow$Error_Rate,xlab = "m",ylab = "Training Error",
legend_fraction_x = 0.2)
}
```

[Package *BoostMLR* version 1.0.3 Index]