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

Uses `rstan`

with pre-compiled Stan code to get posterior draws of parameters from a binary logistic or proportional odds semiparametric ordinal logistic model. The Stan code internally using the qr decompositon on the design matrix so that highly collinear columns of the matrix do not hinder the posterior sampling. The parameters are transformed back to the original scale before returning results to R. Design matrix columns are centered before running Stan, so Stan diagnostic output will have the intercept terms shifted but the results of `blrm()`

for intercepts are for the original uncentered data. The only prior distributions for regression betas are normal with mean zero, and the vector of prior standard deviations is given in `priorsd`

. These priors are for the qr-projected design matrix elements, except that the very last element is not changed. So if one has a single non-interactive linear or binary variable for which a skeptical prior is designed, put that variable last in the model.

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 | ```
blrm(
formula,
ppo = NULL,
cppo = NULL,
keepsep = NULL,
data = environment(formula),
subset,
na.action = na.delete,
priorsd = rep(100, p),
priorsdppo = rep(100, pppo),
iprior = 0,
conc = 1/(0.8 + 0.35 * max(k, 3)),
ascale = 1,
psigma = 1,
rsdmean = if (psigma == 1) 0 else 1,
rsdsd = 1,
normcppo = TRUE,
iter = 2000,
chains = 4,
refresh = 0,
progress = if (refresh > 0) "stan-progress.txt" else "",
x = TRUE,
y = TRUE,
loo = n <= 1000,
ppairs = NULL,
method = c("both", "sampling", "optimizing"),
inito = if (length(ppo)) 0 else "random",
inits = inito,
standata = FALSE,
file = NULL,
debug = FALSE,
...
)
``` |

`formula` |
a R formula object that can use |

`ppo` |
formula specifying the model predictors for which proportional odds is not assumed |

`cppo` |
a function that if present causes a constrained partial PO model to be fit. The function specifies the values in the Gamma vector in Peterson and Harrell (1990) equation (6). To make posterior sampling better behaved, the function should be scaled and centered. This is done by wrapping |

`keepsep` |
a single character string containing a regular expression applied to design matrix column names, specifying which columns are not to be QR-orthonormalized, so that priors for those columns apply to the original parameters. This is useful for treatment and treatment interaction terms. For example |

`data` |
a data frame; defaults to using objects from the calling environment |

`subset` |
a logical vector or integer subscript vector specifying which subset of data whould be used |

`na.action` |
default is |

`priorsd` |
vector of prior standard deviations. If the vector is shorter than the number of model parameters, it will be repeated until the length equals the number of parametertimes. |

`priorsdppo` |
vector of prior standard deviations for non-proportional odds parameters. As with |

`iprior` |
specifies whether to use a Dirichlet distribution for the cell probabilities, which induce a more complex prior distribution for the intercepts ( |

`conc` |
the Dirichlet distribution concentration parameter for the prior distribution of cell probabilities at covariate means. The default is the reciprocal of 0.8 + 0.35 max(k, 3) where k is the number of Y categories. The default is chosen to make the posterior mean of the intercepts more closely match the MLE. For optimizing, the concentration parameter is always 1.0 to obtain results very close to the MLE for providing the posterior mode. |

`ascale` |
scale parameter for the t-distribution for priors for the intercepts if |

`psigma` |
defaults to 1 for a half-t distribution with 4 d.f., location parameter |

`rsdmean` |
the assumed mean of the prior distribution of the standard deviation of random effects. When |

`rsdsd` |
applies only to |

`normcppo` |
set to |

`iter` |
number of posterior samples per chain for |

`chains` |
number of separate chains to run |

`refresh` |
see |

`progress` |
see |

`x` |
set to |

`y` |
set to |

`loo` |
set to |

`ppairs` |
set to a file name to run |

`method` |
set to |

`inito` |
intial value for optimization. The default is the |

`inits` |
initial value for sampling, defaults to |

`standata` |
set to |

`file` |
a file name for a |

`debug` |
set to |

`...` |
passed to |

The partial proportional odds model of Peterson and Harrell (1990) is implemented, and is invoked when the user specifies a second model formula as the `ppo`

argument. This formula has no left-hand-side variable, and has right-side variables that are a subset of those in `formula`

specifying for which predictors the proportional odds assumption is relaxed.

The Peterson and Harrell (1990) constrained partial proportional odds is also implemented, and is usually preferred to the above unconstrained PPO model as it adds a vector of coefficients instead of a matrix of coefficients. In the constrained PPO model the user provides a function `cppo`

that computes a score for all observed values of the dependent variable. For example with a discrete ordinal outcome `cppo`

may return a value of 1.0 for a specific value of Y and zero otherwise. That will result in a departure from the proportional odds assumption for just that one level of Y. The value returned by `cppo`

at the lowest Y value is never used in any case.

`blrm()`

also handles single-level hierarchical random effects models for the case when there are repeated measurements per subject which are reflected as random intercepts, and a different experimental model that allows for AR(1) serial correlation within subject. For both setups, a `cluster`

term in the model signals the existence of subject-specific random effects.

See https://hbiostat.org/R/rms/blrm.html for multiple examples with results.

an `rms`

fit object of class `blrm`

, `rmsb`

, `rms`

that also contains `rstan`

results under the name `rstan`

. In the `rstan`

results, which are also used to produce diagnostics, the intercepts are shifted because of the centering of columns of the design matrix done by `blrm()`

. With `method='optimizing'`

a class-less list is return with these elements: `coefficients`

(MLEs), `beta`

(non-intercept parameters on the QR decomposition scale), `deviance`

(-2 log likelihood), `return_code`

(see `rstan::optimizing()`

), and, if you specified `hessian=TRUE`

to `blrm()`

, the Hessian matrix. To learn about the scaling of orthogonalized QR design matrix columns, look at the `xqrsd`

object in the returned object. This is the vector of SDs for all the columns of the transformed matrix. Those kept out by the `keepsep`

argument will have their original SDs.

Frank Harrell and Ben Goodrich

`print.blrm()`

, `blrmStats()`

, `stanDx()`

, `stanGet()`

, `coef.rmsb()`

, `vcov.rmsb()`

, `print.rmsb()`

, `coef.rmsb()`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
## Not run:
getHdata(Titanic3)
dd <- datadist(titanic3); options(datadist='dd')
f <- blrm(survived ~ (rcs(age, 5) + sex + pclass)^2, data=titanic3)
f # model summary using print.blrm
coef(f) # compute posterior mean parameter values
coef(f, 'median') # compute posterior median values
stanDx(f) # print basic Stan diagnostics
s <- stanGet(f) # extract rstan object from fit
plot(s, pars=f$betas) # Stan posteriors for beta parameters
stanDxplot(s) # Stan diagnostic plots by chain
blrmStats(f) # more details about predictive accuracy measures
ggplot(Predict(...)) # standard rms output
summary(f, ...) # invokes summary.rms
contrast(f, ...) # contrast.rms computes HPD intervals
plot(nomogram(f, ...)) # plot nomogram using posterior mean parameters
# Fit a random effects model to handle multiple observations per
# subject ID
f <- blrm(outcome ~ rcs(age, 5) + sex + cluster(id), data=mydata)
## End(Not run)
``` |

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