Package 'bkmr'

Title:	Bayesian Kernel Machine Regression
Description:	Implementation of a statistical approach for estimating the joint health effects of multiple concurrent exposures, as described in Bobb et al (2015) <doi:10.1093/biostatistics/kxu058>.
Authors:	Jennifer F. Bobb [aut, cre]
Maintainer:	Jennifer F. Bobb <[email protected]>
License:	GPL-2
Version:	0.2.2
Built:	2024-10-10 04:44:10 UTC
Source:	https://github.com/jenfb/bkmr

Help Index

Compute the posterior mean and variance of h at a new predictor values
Extract summary statistics
Extract posterior inclusion probabilities (PIPs) from BKMR model fit
Extract samples
Investigate prior
Fit Bayesian kernel machine regression
Calculate overall risk summaries
Plot of exposure-response function from univariate KMR fit
Predict the exposure-response function at a new grid of points
Plot cross-sections of the bivariate predictor-response function
Plot bivariate predictor-response function on a new grid of points
Plot univariate predictor-response function on a new grid of points
Print basic summary of BKMR model fit
Obtain posterior samples of predictions at new points
Simulate dataset
Single Variable Interaction Summaries
Single Variable Risk Summaries
Summarizing BKMR model fits
Trace plot

Compute the posterior mean and variance of `h` at a new predictor values

Description

Compute the posterior mean and variance of h at a new predictor values

Usage

ComputePostmeanHnew(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  Znew = NULL,
  sel = NULL,
  method = "approx"
)
ComputePostmeanHnew(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  Znew = NULL,
  sel = NULL,
  method = "approx"
)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`y`	a vector of outcome data of length `n`.
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`X`	an `n`-by-`K` matrix of covariate data where each row represents an observation and each column represents a covariate. Should not contain an intercept column.
`Znew`	matrix of new predictor values at which to predict new `h`, where each row represents a new observation. If set to NULL then will default to using the observed exposures Z.
`sel`	selects which iterations of the MCMC sampler to use for inference; see details
`method`	method for obtaining posterior summaries at a vector of new points. Options are "approx" and "exact"; defaults to "approx", which is faster particularly for large datasets; see details

Details

If method == "approx", the argument sel defaults to the second half of the MCMC iterations.
If method == "exact", the argument sel defaults to keeping every 10 iterations after dropping the first 50% of samples, or if this results in fewer than 100 iterations, than 100 iterations are kept

For guided examples and additional information, go to https://jenfb.github.io/bkmr/overview.html

Value

a list of length two containing the posterior mean vector and posterior variance matrix

Examples

set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

med_vals <- apply(Z, 2, median)
Znew <- matrix(med_vals, nrow = 1)
h_true <- dat$HFun(Znew)
h_est1 <- ComputePostmeanHnew(fitkm, Znew = Znew, method = "approx")
h_est2 <- ComputePostmeanHnew(fitkm, Znew = Znew, method = "exact")
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

med_vals <- apply(Z, 2, median)
Znew <- matrix(med_vals, nrow = 1)
h_true <- dat$HFun(Znew)
h_est1 <- ComputePostmeanHnew(fitkm, Znew = Znew, method = "approx")
h_est2 <- ComputePostmeanHnew(fitkm, Znew = Znew, method = "exact")

Extract summary statistics

Description

Obtain summary statistics of each parameter from the BKMR fit

Usage

ExtractEsts(fit, q = c(0.025, 0.25, 0.5, 0.75, 0.975), sel = NULL)
ExtractEsts(fit, q = c(0.025, 0.25, 0.5, 0.75, 0.975), sel = NULL)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`q`	vector of quantiles
`sel`	logical expression indicating samples to keep; defaults to keeping the second half of all samples

Value

a list where each component is a data frame containing the summary statistics of the posterior distribution of one of the parameters (or vector of parameters) being estimated

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

ests <- ExtractEsts(fitkm)
names(ests)
ests$beta
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

ests <- ExtractEsts(fitkm)
names(ests)
ests$beta

Extract posterior inclusion probabilities (PIPs) from BKMR model fit

Description

Extract posterior inclusion probabilities (PIPs) from Bayesian Kernel Machine Regression (BKMR) model fit

Usage

ExtractPIPs(fit, sel = NULL, z.names = NULL)
ExtractPIPs(fit, sel = NULL, z.names = NULL)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`sel`	logical expression indicating samples to keep; defaults to keeping the second half of all samples
`z.names`	optional argument providing the names of the variables included in the `h` function.

Details

For guided examples, go to https://jenfb.github.io/bkmr/overview.html

Value

a data frame with the variable-specific PIPs for BKMR fit with component-wise variable selection, and with the group-specific and conditional (within-group) PIPs for BKMR fit with hierarchical variable selection.

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

ExtractPIPs(fitkm)
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

ExtractPIPs(fitkm)

Extract samples

Description

Extract samples of each parameter from the BKMR fit

Usage

ExtractSamps(fit, sel = NULL)
ExtractSamps(fit, sel = NULL)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`sel`	logical expression indicating samples to keep; defaults to keeping the second half of all samples

Value

a list where each component contains the posterior samples of one of the parameters (or vector of parameters) being estimated

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

samps <- ExtractSamps(fitkm)
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

samps <- ExtractSamps(fitkm)

Investigate prior

Description

Investigate the impact of the r[m] parameters on the smoothness of the exposure-response function h(z[m]).

Usage

InvestigatePrior(
  y,
  Z,
  X,
  ngrid = 50,
  q.seq = c(2, 1, 1/2, 1/4, 1/8, 1/16),
  r.seq = NULL,
  Drange = NULL,
  verbose = FALSE
)
InvestigatePrior(
  y,
  Z,
  X,
  ngrid = 50,
  q.seq = c(2, 1, 1/2, 1/4, 1/8, 1/16),
  r.seq = NULL,
  Drange = NULL,
  verbose = FALSE
)

Arguments

`y`	a vector of outcome data of length `n`.
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`X`	an `n`-by-`K` matrix of covariate data where each row represents an observation and each column represents a covariate. Should not contain an intercept column.
`ngrid`	Number of grid points over which to plot the exposure-response function
`q.seq`	Sequence of values corresponding to different degrees of smoothness in the estimated exposure-response function. A value of q corresponds to fractions of the range of the data over which there is a decay in the correlation `cor(h[i],h[j])` between two subjects by 50`%`.
`r.seq`	sequence of values at which to fix `r` for estimating the exposure-response function
`Drange`	the range of the `z_m` data over which to apply the values of `q.seq`. If not specified, will be calculated as the maximum of the ranges of `z_1` through `z_M`.
`verbose`	TRUE or FALSE: flag indicating whether to print to the screen which exposure variable and q value has been completed

Details

For guided examples, go to https://jenfb.github.io/bkmr/overview.html

Value

a list containing the predicted values, residuals, and estimated predictor-response function for each degree of smoothness being considered

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

priorfits <- InvestigatePrior(y = y, Z = Z, X = X, q.seq = c(2, 1/2, 1/4, 1/16))
PlotPriorFits(y = y, Z = Z, X = X, fits = priorfits)
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

priorfits <- InvestigatePrior(y = y, Z = Z, X = X, q.seq = c(2, 1/2, 1/4, 1/16))
PlotPriorFits(y = y, Z = Z, X = X, fits = priorfits)

Fit Bayesian kernel machine regression

Description

Fits the Bayesian kernel machine regression (BKMR) model using Markov chain Monte Carlo (MCMC) methods.

Usage

kmbayes(
  y,
  Z,
  X = NULL,
  iter = 1000,
  family = "gaussian",
  id = NULL,
  verbose = TRUE,
  Znew = NULL,
  starting.values = NULL,
  control.params = NULL,
  varsel = FALSE,
  groups = NULL,
  knots = NULL,
  ztest = NULL,
  rmethod = "varying",
  est.h = FALSE
)
kmbayes(
  y,
  Z,
  X = NULL,
  iter = 1000,
  family = "gaussian",
  id = NULL,
  verbose = TRUE,
  Znew = NULL,
  starting.values = NULL,
  control.params = NULL,
  varsel = FALSE,
  groups = NULL,
  knots = NULL,
  ztest = NULL,
  rmethod = "varying",
  est.h = FALSE
)

Arguments

`y`	a vector of outcome data of length `n`.
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`X`	an `n`-by-`K` matrix of covariate data where each row represents an observation and each column represents a covariate. Should not contain an intercept column.
`iter`	number of iterations to run the sampler
`family`	a description of the error distribution and link function to be used in the model. Currently implemented for `gaussian` and `binomial` families.
`id`	optional vector (of length `n`) of grouping factors for fitting a model with a random intercept. If NULL then no random intercept will be included.
`verbose`	TRUE or FALSE: flag indicating whether to print intermediate diagnostic information during the model fitting.
`Znew`	optional matrix of new predictor values at which to predict `h`, where each row represents a new observation. This will slow down the model fitting, and can be done as a post-processing step using `SamplePred`
`starting.values`	list of starting values for each parameter. If not specified default values will be chosen.
`control.params`	list of parameters specifying the prior distributions and tuning parameters for the MCMC algorithm. If not specified default values will be chosen.
`varsel`	TRUE or FALSE: indicator for whether to conduct variable selection on the Z variables in `h`
`groups`	optional vector (of length `M`) of group indicators for fitting hierarchical variable selection if varsel=TRUE. If varsel=TRUE without group specification, component-wise variable selections will be performed.
`knots`	optional matrix of knot locations for implementing the Gaussian predictive process of Banerjee et al. (2008). Currently only implemented for models without a random intercept.
`ztest`	optional vector indicating on which variables in Z to conduct variable selection (the remaining variables will be forced into the model).
`rmethod`	for those predictors being forced into the `h` function, the method for sampling the `r[m]` values. Takes the value of 'varying' to allow separate `r[m]` for each predictor; 'equal' to force the same `r[m]` for each predictor; or 'fixed' to fix the `r[m]` to their starting values
`est.h`	TRUE or FALSE: indicator for whether to sample from the posterior distribution of the subject-specific effects h_i within the main sampler. This will slow down the model fitting.

Value

an object of class "bkmrfit" (containing the posterior samples from the model fit), which has the associated methods:

print (i.e., print.bkmrfit)
summary (i.e., summary.bkmrfit)

References

Bobb, JF, Valeri L, Claus Henn B, Christiani DC, Wright RO, Mazumdar M, Godleski JJ, Coull BA (2015). Bayesian Kernel Machine Regression for Estimating the Health Effects of Multi-Pollutant Mixtures. Biostatistics 16, no. 3: 493-508.

Banerjee S, Gelfand AE, Finley AO, Sang H (2008). Gaussian predictive process models for large spatial data sets. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(4), 825-848.

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

Calculate overall risk summaries

Description

Compare estimated h function when all predictors are at a particular quantile to when all are at a second fixed quantile

Usage

OverallRiskSummaries(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  qs = seq(0.25, 0.75, by = 0.05),
  q.fixed = 0.5,
  method = "approx",
  sel = NULL
)
OverallRiskSummaries(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  qs = seq(0.25, 0.75, by = 0.05),
  q.fixed = 0.5,
  method = "approx",
  sel = NULL
)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`y`	a vector of outcome data of length `n`.
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`X`	an `n`-by-`K` matrix of covariate data where each row represents an observation and each column represents a covariate. Should not contain an intercept column.
`qs`	vector of quantiles at which to calculate the overall risk summary
`q.fixed`	a second quantile at which to compare the estimated `h` function
`method`	method for obtaining posterior summaries at a vector of new points. Options are "approx" and "exact"; defaults to "approx", which is faster particularly for large datasets; see details
`sel`	selects which iterations of the MCMC sampler to use for inference; see details

Details

If method == "approx", the argument sel defaults to the second half of the MCMC iterations.
If method == "exact", the argument sel defaults to keeping every 10 iterations after dropping the first 50% of samples, or if this results in fewer than 100 iterations, than 100 iterations are kept

For guided examples and additional information, go to https://jenfb.github.io/bkmr/overview.html

Value

a data frame containing the (posterior mean) estimate and posterior standard deviation of the overall risk measures

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

risks.overall <- OverallRiskSummaries(fit = fitkm, qs = seq(0.25, 0.75, by = 0.05), 
q.fixed = 0.5, method = "exact")
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

risks.overall <- OverallRiskSummaries(fit = fitkm, qs = seq(0.25, 0.75, by = 0.05), 
q.fixed = 0.5, method = "exact")

Plot of exposure-response function from univariate KMR fit

Description

Plot the estimated h(z[m]) estimated from frequentist KMR for r[m] fixed to specific values

Usage

PlotPriorFits(
  y,
  X,
  Z,
  fits,
  which.z = NULL,
  which.q = NULL,
  plot.resid = TRUE,
  ylim = NULL,
  ...
)
PlotPriorFits(
  y,
  X,
  Z,
  fits,
  which.z = NULL,
  which.q = NULL,
  plot.resid = TRUE,
  ylim = NULL,
  ...
)

Arguments

`y`	a vector of outcome data of length `n`.
`X`	an `n`-by-`K` matrix of covariate data where each row represents an observation and each column represents a covariate. Should not contain an intercept column.
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`fits`	output from `InvestigatePrior`
`which.z`	which predictors (columns in `Z`) to plot
`which.q`	which q.values to plot; defaults to all possible
`plot.resid`	whether to plot the data points
`ylim`	plotting limits for the y-axis
`...`	other plotting arguments

Value

No return value, generates plot

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

priorfits <- InvestigatePrior(y = y, Z = Z, X = X, q.seq = c(2, 1/2, 1/4, 1/16))
PlotPriorFits(y = y, Z = Z, X = X, fits = priorfits)
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

priorfits <- InvestigatePrior(y = y, Z = Z, X = X, q.seq = c(2, 1/2, 1/4, 1/16))
PlotPriorFits(y = y, Z = Z, X = X, fits = priorfits)

Predict the exposure-response function at a new grid of points

Description

Predict the exposure-response function at a new grid of points

Usage

PredictorResponseBivar(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  z.pairs = NULL,
  method = "approx",
  ngrid = 50,
  q.fixed = 0.5,
  sel = NULL,
  min.plot.dist = 0.5,
  center = TRUE,
  z.names = colnames(Z),
  verbose = TRUE,
  ...
)
PredictorResponseBivar(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  z.pairs = NULL,
  method = "approx",
  ngrid = 50,
  q.fixed = 0.5,
  sel = NULL,
  min.plot.dist = 0.5,
  center = TRUE,
  z.names = colnames(Z),
  verbose = TRUE,
  ...
)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`y`	a vector of outcome data of length `n`.
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`X`	an `n`-by-`K` matrix of covariate data where each row represents an observation and each column represents a covariate. Should not contain an intercept column.
`z.pairs`	data frame showing which pairs of predictors to plot
`method`	method for obtaining posterior summaries at a vector of new points. Options are "approx" and "exact"; defaults to "approx", which is faster particularly for large datasets; see details
`ngrid`	number of grid points in each dimension
`q.fixed`	vector of quantiles at which to fix the remaining predictors in `Z`
`sel`	logical expression indicating samples to keep; defaults to keeping the second half of all samples
`min.plot.dist`	specifies a minimum distance that a new grid point needs to be from an observed data point in order to compute the prediction; points further than this will not be computed
`center`	flag for whether to scale the exposure-response function to have mean zero
`z.names`	optional vector of names for the columns of `z`
`verbose`	TRUE or FALSE: flag of whether to print intermediate output to the screen
`...`	other arguments to pass on to the prediction function

Details

For guided examples, go to https://jenfb.github.io/bkmr/overview.html

Value

a long data frame with the name of the first predictor, the name of the second predictor, the value of the first predictor, the value of the second predictor, the posterior mean estimate, and the posterior standard deviation of the estimated exposure response function

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

## Obtain predicted value on new grid of points for each pair of predictors
## Using only a 10-by-10 point grid to make example run quickly
pred.resp.bivar <- PredictorResponseBivar(fit = fitkm, min.plot.dist = 1, ngrid = 10)

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

## Obtain predicted value on new grid of points for each pair of predictors
## Using only a 10-by-10 point grid to make example run quickly
pred.resp.bivar <- PredictorResponseBivar(fit = fitkm, min.plot.dist = 1, ngrid = 10)

Plot cross-sections of the bivariate predictor-response function

Description

Function to plot the h function of a particular variable at different levels (quantiles) of a second variable

Usage

PredictorResponseBivarLevels(
  pred.resp.df,
  Z = NULL,
  qs = c(0.25, 0.5, 0.75),
  both_pairs = TRUE,
  z.names = NULL
)
PredictorResponseBivarLevels(
  pred.resp.df,
  Z = NULL,
  qs = c(0.25, 0.5, 0.75),
  both_pairs = TRUE,
  z.names = NULL
)

Arguments

`pred.resp.df`	object obtained from running the function `PredictorResponseBivar`
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`qs`	vector of quantiles at which to fix the second variable
`both_pairs`	flag indicating whether, if `h(z1)` is being plotted for z2 fixed at different levels, that they should be plotted in the reverse order as well (for `h(z2)` at different levels of z1)
`z.names`	optional vector of names for the columns of `z`

Details

For guided examples, go to https://jenfb.github.io/bkmr/overview.html

Value

a long data frame with the name of the first predictor, the name of the second predictor, the value of the first predictor, the quantile at which the second predictor is fixed, the posterior mean estimate, and the posterior standard deviation of the estimated exposure response function

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

## Obtain predicted value on new grid of points for each pair of predictors
## Using only a 10-by-10 point grid to make example run quickly
pred.resp.bivar <- PredictorResponseBivar(fit = fitkm, min.plot.dist = 1, ngrid = 10)
pred.resp.bivar.levels <- PredictorResponseBivarLevels(pred.resp.df = pred.resp.bivar, 
Z = Z, qs = c(0.1, 0.5, 0.9))
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

## Obtain predicted value on new grid of points for each pair of predictors
## Using only a 10-by-10 point grid to make example run quickly
pred.resp.bivar <- PredictorResponseBivar(fit = fitkm, min.plot.dist = 1, ngrid = 10)
pred.resp.bivar.levels <- PredictorResponseBivarLevels(pred.resp.df = pred.resp.bivar, 
Z = Z, qs = c(0.1, 0.5, 0.9))

Plot bivariate predictor-response function on a new grid of points

Description

Plot bivariate predictor-response function on a new grid of points

Usage

PredictorResponseBivarPair(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  whichz1 = 1,
  whichz2 = 2,
  whichz3 = NULL,
  method = "approx",
  prob = 0.5,
  q.fixed = 0.5,
  sel = NULL,
  ngrid = 50,
  min.plot.dist = 0.5,
  center = TRUE,
  ...
)
PredictorResponseBivarPair(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  whichz1 = 1,
  whichz2 = 2,
  whichz3 = NULL,
  method = "approx",
  prob = 0.5,
  q.fixed = 0.5,
  sel = NULL,
  ngrid = 50,
  min.plot.dist = 0.5,
  center = TRUE,
  ...
)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`y`	a vector of outcome data of length `n`.
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`X`	an `n`-by-`K` matrix of covariate data where each row represents an observation and each column represents a covariate. Should not contain an intercept column.
`whichz1`	vector identifying the first predictor that (column of `Z`) should be plotted
`whichz2`	vector identifying the second predictor that (column of `Z`) should be plotted
`whichz3`	vector identifying the third predictor that will be set to a pre-specified fixed quantile (determined by `prob`)
`method`	method for obtaining posterior summaries at a vector of new points. Options are "approx" and "exact"; defaults to "approx", which is faster particularly for large datasets; see details
`prob`	pre-specified quantile to set the third predictor (determined by `whichz3`); defaults to 0.5 (50th percentile)
`q.fixed`	vector of quantiles at which to fix the remaining predictors in `Z`
`sel`	logical expression indicating samples to keep; defaults to keeping the second half of all samples
`ngrid`	number of grid points to cover the range of each predictor (column in `Z`)
`min.plot.dist`	specifies a minimum distance that a new grid point needs to be from an observed data point in order to compute the prediction; points further than this will not be computed
`center`	flag for whether to scale the exposure-response function to have mean zero
`...`	other arguments to pass on to the prediction function

Value

a data frame with value of the first predictor, the value of the second predictor, the posterior mean estimate, and the posterior standard deviation

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

## Obtain predicted value on new grid of points
## Using only a 10-by-10 point grid to make example run quickly
pred.resp.bivar12 <- PredictorResponseBivarPair(fit = fitkm, min.plot.dist = 1, ngrid = 10)
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

## Obtain predicted value on new grid of points
## Using only a 10-by-10 point grid to make example run quickly
pred.resp.bivar12 <- PredictorResponseBivarPair(fit = fitkm, min.plot.dist = 1, ngrid = 10)

Plot univariate predictor-response function on a new grid of points

Description

Plot univariate predictor-response function on a new grid of points

Usage

PredictorResponseUnivar(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  which.z = 1:ncol(Z),
  method = "approx",
  ngrid = 50,
  q.fixed = 0.5,
  sel = NULL,
  min.plot.dist = Inf,
  center = TRUE,
  z.names = colnames(Z),
  ...
)
PredictorResponseUnivar(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  which.z = 1:ncol(Z),
  method = "approx",
  ngrid = 50,
  q.fixed = 0.5,
  sel = NULL,
  min.plot.dist = Inf,
  center = TRUE,
  z.names = colnames(Z),
  ...
)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`y`	a vector of outcome data of length `n`.
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`X`	an `n`-by-`K` matrix of covariate data where each row represents an observation and each column represents a covariate. Should not contain an intercept column.
`which.z`	vector identifying which predictors (columns of `Z`) should be plotted
`method`	method for obtaining posterior summaries at a vector of new points. Options are "approx" and "exact"; defaults to "approx", which is faster particularly for large datasets; see details
`ngrid`	number of grid points to cover the range of each predictor (column in `Z`)
`q.fixed`	vector of quantiles at which to fix the remaining predictors in `Z`
`sel`	logical expression indicating samples to keep; defaults to keeping the second half of all samples
`min.plot.dist`	specifies a minimum distance that a new grid point needs to be from an observed data point in order to compute the prediction; points further than this will not be computed
`center`	flag for whether to scale the exposure-response function to have mean zero
`z.names`	optional vector of names for the columns of `z`
`...`	other arguments to pass on to the prediction function

Details

For guided examples, go to https://jenfb.github.io/bkmr/overview.html

Value

a long data frame with the predictor name, predictor value, posterior mean estimate, and posterior standard deviation

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)
pred.resp.univar <- PredictorResponseUnivar(fit = fitkm)
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)
pred.resp.univar <- PredictorResponseUnivar(fit = fitkm)

Print basic summary of BKMR model fit

Description

print method for class "bkmrfit"

Usage

## S3 method for class 'bkmrfit'
print(x, digits = 5, ...)
## S3 method for class 'bkmrfit'
print(x, digits = 5, ...)

Arguments

`x`	an object of class "bkmrfit"
`digits`	the number of digits to show when printing
`...`	further arguments passed to or from other methods.

Value

No return value, prints basic summary of fit to console

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)
fitkm
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)
fitkm

Obtain posterior samples of predictions at new points

Description

Obtains posterior samples of E(Y) = h(Znew) + beta*Xnew or of g^{-1}[E(y)]

Usage

SamplePred(
  fit,
  Znew = NULL,
  Xnew = NULL,
  Z = NULL,
  X = NULL,
  y = NULL,
  sel = NULL,
  type = c("link", "response"),
  ...
)
SamplePred(
  fit,
  Znew = NULL,
  Xnew = NULL,
  Z = NULL,
  X = NULL,
  y = NULL,
  sel = NULL,
  type = c("link", "response"),
  ...
)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`Znew`	optional matrix of new predictor values at which to predict new `h`, where each row represents a new observation. If not specified, defaults to using observed Z values
`Xnew`	optional matrix of new covariate values at which to obtain predictions. If not specified, defaults to using observed X values
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`X`	an `n`-by-`K` matrix of covariate data where each row represents an observation and each column represents a covariate. Should not contain an intercept column.
`y`	a vector of outcome data of length `n`.
`sel`	A vector selecting which iterations of the BKMR fit should be retained for inference. If not specified, will default to keeping every 10 iterations after dropping the first 50% of samples, or if this results in fewer than 100 iterations, than 100 iterations are kept
`type`	whether to make predictions on the scale of the link or of the response; only relevant for the binomial outcome family
`...`	other arguments; not currently used

Details

For guided examples, go to https://jenfb.github.io/bkmr/overview.html

Value

a matrix with the posterior samples at the new points

Examples

set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

med_vals <- apply(Z, 2, median)
Znew <- matrix(med_vals, nrow = 1)
h_true <- dat$HFun(Znew)
set.seed(111)
samps3 <- SamplePred(fitkm, Znew = Znew, Xnew = cbind(0))
head(samps3)
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

med_vals <- apply(Z, 2, median)
Znew <- matrix(med_vals, nrow = 1)
h_true <- dat$HFun(Znew)
set.seed(111)
samps3 <- SamplePred(fitkm, Znew = Znew, Xnew = cbind(0))
head(samps3)

Simulate dataset

Description

Simulate predictor, covariate, and continuous outcome data

Usage

SimData(
  n = 100,
  M = 5,
  sigsq.true = 0.5,
  beta.true = 2,
  hfun = 3,
  Zgen = "norm",
  ind = 1:2,
  family = "gaussian"
)
SimData(
  n = 100,
  M = 5,
  sigsq.true = 0.5,
  beta.true = 2,
  hfun = 3,
  Zgen = "norm",
  ind = 1:2,
  family = "gaussian"
)

Arguments

`n`	Number of observations
`M`	Number of predictor variables to generate
`sigsq.true`	Variance of normally distributed residual error
`beta.true`	Coefficient on the covariate
`hfun`	An integer from 1 to 3 identifying which predictor-response function to generate
`Zgen`	Method for generating the matrix Z of exposure variables, taking one of the values c("unif", "norm", "corr", "realistic")
`ind`	select which predictor(s) will be included in the `h` function; how many predictors that can be included will depend on which `h` function is being used.
`family`	a description of the error distribution and link function to be used in the model. Currently implemented for `gaussian` and `binomial` families.

Details

hfun = 1: A nonlinear function of the first predictor
hfun = 2: A linear function of the first two predictors and their product term
hfun = 3: A nonlinear and nonadditive function of the first two predictor variables

Value

a list containing the parameter values and generated variables of the simulated datasets

Examples

set.seed(5)
dat <- SimData()
set.seed(5)
dat <- SimData()

Single Variable Interaction Summaries

Description

Compare the single-predictor health risks when all of the other predictors in Z are fixed to their a specific quantile to when all of the other predictors in Z are fixed to their a second specific quantile.

Usage

SingVarIntSummaries(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  which.z = 1:ncol(Z),
  qs.diff = c(0.25, 0.75),
  qs.fixed = c(0.25, 0.75),
  method = "approx",
  sel = NULL,
  z.names = colnames(Z),
  ...
)
SingVarIntSummaries(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  which.z = 1:ncol(Z),
  qs.diff = c(0.25, 0.75),
  qs.fixed = c(0.25, 0.75),
  method = "approx",
  sel = NULL,
  z.names = colnames(Z),
  ...
)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`y`	a vector of outcome data of length `n`.
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`X`	an `n`-by-`K` matrix of covariate data where each row represents an observation and each column represents a covariate. Should not contain an intercept column.
`which.z`	vector indicating which variables (columns of `Z`) for which the summary should be computed
`qs.diff`	vector indicating the two quantiles at which to compute the single-predictor risk summary
`qs.fixed`	vector indicating the two quantiles at which to fix all of the remaining exposures in `Z`
`method`	method for obtaining posterior summaries at a vector of new points. Options are "approx" and "exact"; defaults to "approx", which is faster particularly for large datasets; see details
`sel`	logical expression indicating samples to keep; defaults to keeping the second half of all samples
`z.names`	optional vector of names for the columns of `z`
`...`	other arguments to pass on to the prediction function

Details

If method == "approx", the argument sel defaults to the second half of the MCMC iterations.
If method == "exact", the argument sel defaults to keeping every 10 iterations after dropping the first 50% of samples, or if this results in fewer than 100 iterations, than 100 iterations are kept

For guided examples and additional information, go to https://jenfb.github.io/bkmr/overview.html

Value

a data frame containing the (posterior mean) estimate and posterior standard deviation of the single-predictor risk measures

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

risks.int <- SingVarIntSummaries(fit = fitkm, method = "exact")
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

risks.int <- SingVarIntSummaries(fit = fitkm, method = "exact")

Single Variable Risk Summaries

Description

Compute summaries of the risks associated with a change in a single variable in Z from a single level (quantile) to a second level (quantile), for the other variables in Z fixed to a specific level (quantile)

Usage

SingVarRiskSummaries(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  which.z = 1:ncol(Z),
  qs.diff = c(0.25, 0.75),
  q.fixed = c(0.25, 0.5, 0.75),
  method = "approx",
  sel = NULL,
  z.names = colnames(Z),
  ...
)
SingVarRiskSummaries(
  fit,
  y = NULL,
  Z = NULL,
  X = NULL,
  which.z = 1:ncol(Z),
  qs.diff = c(0.25, 0.75),
  q.fixed = c(0.25, 0.5, 0.75),
  method = "approx",
  sel = NULL,
  z.names = colnames(Z),
  ...
)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`y`	a vector of outcome data of length `n`.
`Z`	an `n`-by-`M` matrix of predictor variables to be included in the `h` function. Each row represents an observation and each column represents an predictor.
`X`	an `n`-by-`K` matrix of covariate data where each row represents an observation and each column represents a covariate. Should not contain an intercept column.
`which.z`	vector indicating which variables (columns of `Z`) for which the summary should be computed
`qs.diff`	vector indicating the two quantiles `q_1` and `q_2` at which to compute `h(z_{q2}) - h(z_{q1})`
`q.fixed`	vector of quantiles at which to fix the remaining predictors in `Z`
`method`	method for obtaining posterior summaries at a vector of new points. Options are "approx" and "exact"; defaults to "approx", which is faster particularly for large datasets; see details
`sel`	logical expression indicating samples to keep; defaults to keeping the second half of all samples
`z.names`	optional vector of names for the columns of `z`
`...`	other arguments to pass on to the prediction function

Details

If method == "approx", the argument sel defaults to the second half of the MCMC iterations.
If method == "exact", the argument sel defaults to keeping every 10 iterations after dropping the first 50% of samples, or if this results in fewer than 100 iterations, than 100 iterations are kept

For guided examples and additional information, go to https://jenfb.github.io/bkmr/overview.html

Value

a data frame containing the (posterior mean) estimate and posterior standard deviation of the single-predictor risk measures

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

risks.singvar <- SingVarRiskSummaries(fit = fitkm, method = "exact")
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

risks.singvar <- SingVarRiskSummaries(fit = fitkm, method = "exact")

Summarizing BKMR model fits

Description

summary method for class "bkmrfit"

Usage

## S3 method for class 'bkmrfit'
summary(
  object,
  q = c(0.025, 0.975),
  digits = 5,
  show_ests = TRUE,
  show_MH = TRUE,
  ...
)
## S3 method for class 'bkmrfit'
summary(
  object,
  q = c(0.025, 0.975),
  digits = 5,
  show_ests = TRUE,
  show_MH = TRUE,
  ...
)

Arguments

`object`	an object of class "bkmrfit"
`q`	quantiles of posterior distribution to show
`digits`	the number of digits to show when printing
`show_ests`	logical; if `TRUE`, prints summary statistics of posterior distribution
`show_MH`	logical; if `TRUE`, prints acceptance rates from the Metropolis-Hastings algorithm
`...`	further arguments passed to or from other methods.

Value

No return value, prints more detailed summary of fit to console

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)
summary(fitkm)
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)
summary(fitkm)

Trace plot

Description

Trace plot

Usage

TracePlot(
  fit,
  par,
  comp = 1,
  sel = NULL,
  main = "",
  xlab = "iteration",
  ylab = "parameter value",
  ...
)
TracePlot(
  fit,
  par,
  comp = 1,
  sel = NULL,
  main = "",
  xlab = "iteration",
  ylab = "parameter value",
  ...
)

Arguments

`fit`	An object containing the results returned by a the `kmbayes` function
`par`	which parameter to plot
`comp`	which component of the parameter vector to plot
`sel`	logical expression indicating samples to keep; defaults to keeping the second half of all samples
`main`	title
`xlab`	x axis label
`ylab`	y axis label
`...`	other arguments to pass onto the plotting function

Details

For guided examples, go to https://jenfb.github.io/bkmr/overview.html

Value

No return value, generates plot

Examples

## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

TracePlot(fit = fitkm, par = "beta")
TracePlot(fit = fitkm, par = "sigsq.eps")
TracePlot(fit = fitkm, par = "r", comp = 1)
## First generate dataset
set.seed(111)
dat <- SimData(n = 50, M = 4)
y <- dat$y
Z <- dat$Z
X <- dat$X

## Fit model with component-wise variable selection
## Using only 100 iterations to make example run quickly
## Typically should use a large number of iterations for inference
set.seed(111)
fitkm <- kmbayes(y = y, Z = Z, X = X, iter = 100, verbose = FALSE, varsel = TRUE)

TracePlot(fit = fitkm, par = "beta")
TracePlot(fit = fitkm, par = "sigsq.eps")
TracePlot(fit = fitkm, par = "r", comp = 1)

Package 'bkmr'

Help Index

Compute the posterior mean and variance of h at a new predictor values

Description

Usage

Arguments

Details

Value

Examples

Extract summary statistics

Description

Usage

Arguments

Value

Examples

Extract posterior inclusion probabilities (PIPs) from BKMR model fit

Description

Usage

Arguments

Details

Value

Examples

Extract samples

Description

Usage

Arguments

Value

Examples

Investigate prior

Description

Usage

Arguments

Details

Value

Examples

Fit Bayesian kernel machine regression

Description

Usage

Arguments

Value

References

See Also

Examples

Calculate overall risk summaries

Description

Usage

Arguments

Details

Value

Examples

Plot of exposure-response function from univariate KMR fit

Description

Usage

Arguments

Value

Examples

Predict the exposure-response function at a new grid of points

Description

Usage

Arguments

Details

Value

Examples

Plot cross-sections of the bivariate predictor-response function

Description

Usage

Arguments

Details

Value

Examples

Plot bivariate predictor-response function on a new grid of points

Description

Usage

Arguments

Value

Examples

Plot univariate predictor-response function on a new grid of points

Description

Usage

Arguments

Compute the posterior mean and variance of `h` at a new predictor values