a data frame or a matrix, with the dependent variable in the first column, followed by the covariates (alternatively, X.data can also be provided as a formula). Note that bms automatically estimates a constant, therefore including constant terms is not necessary.

The (positive integer) number of burn-in draws for the MC3 sampler, defaults to 1000. (Not taken into account if mcmc="enumerate")

If mcmc is set to an MC3 sampler, then this is the number of iteration draws to be sampled (ex burn-ins), default 3000 draws.
If mcmc="enumerate", then iter is the number of models to be sampled, starting from 0 (defaults to 2^K-1) - cf. start.value.

the number of best models for which information is stored (default 500). Best models are used for convergence analysis between likelihoods and MCMC frequencies, as well as likelihood-based inference.
Note that a very high value for nmodel slows down the sampler significantly. Set nmodel=0 to speed up sampling (if best model information is not needed).

a character denoting the model sampler to be used.
The MC3 sampler mcmc="bd" corresponds to a birth/death MCMC algogrithm. mcmc="rev.jump" enacts a reversible jump algorithm adding a "swap" step to the birth / death steps from "bd".
Alternatively, the entire model space may be fully enumerated by setting mcmc="enumerate" which will iterate all possible regressor combinations (Note: consider that this means 2^K iterations, where K is the number of covariates.)
Default is full enumeration (mcmc="enumerate") with less then 15 covariates, and the birth-death MC3 sampler (mcmc="bd") with 15 covariates or more. Cf. section 'Details' for more options.

the hyperparameter on Zellner's g-prior for the regression coefficients.
g="UIP" corresponds to g=N, the number of observations (default);
g="BRIC" corresponds to the benchmark prior suggested by Fernandez, Ley and Steel (2001), i.e g=max(N, K^2), where K is the total number of covariates;
g="RIC" sets g=K^2 and conforms to the risk inflation criterion by George and Foster (1994)
g="HQ" sets g=log(N)^3 and asymptotically mimics the Hannan-Quinn criterion with C_{HQ}=3 (cf. Fernandez, Ley and Steel, 2001, p.395)
g="EBL" estimates a local empirical Bayes g-parameter (as in Liang et al. (2008));
g="hyper" takes the 'hyper-g' prior distribution (as in Liang et al., 2008) with the default hyper-parameter a set such that the prior expected shrinkage factor conforms to 'UIP';
This hyperparameter a can be adjusted (between 2<a<=4) by setting g="hyper=2.9", for instance.
Alternatively, g="hyper=UIP" sets the prior expected value of the shrinkage factor equal to that of UIP (default), g="hyper=BRIC" sets it according to BRIC
cf section 'Details' fro more on the hyper-g prior

a character denoting the model prior choice, defaulting to "random":
mprior="fixed" denotes fixed common prior inclusion probabilities for each regressor as e.g. in Sala-i-Martin, Doppelhofer, and Miller(2004) - for their fine-tuning, cf. mprior.size. Preferable to mcmc="random" if strong prior information on model size exists;
mprior="random" (default) triggers the 'random theta' prior by Ley and Steel (2008), who suggest a binomial-beta hyperprior on the a priori inclusion probability;
mprior="uniform" employs the uniform model prior;
mprior="customk" allows for custom model size priors (cf. mprior.size);
mprior="pip" allows for custom prior inclusion probabilities (cf. mprior.size);
Note that the prior on models with more than N-3 regressors is automatically zero: these models will not be sampled.

if mprior is "fixed" or "random", mprior.size is a scalar that denotes the prior expected value of the model size prior (default K/2).
If mprior="customk" then a custom model size prior can be provided as a K+1 vector detailing the priors from model size 0 to K (e.g. rep(1,K+1) for the uniform model prior);
if mprior="pip", then custom prior inclusion probabilities can be provided as a vector of size K, with elements in the interval (0,1)

'interactive mode': print out results to console after ending the routine and plots a chart (default TRUE).

specifies the starting model of the iteration chain. For instance a specific model by the corresponding column indices (e.g. starting.model=numeric(K) starts from the null model including solely a constant term) or start.value=c(3,6) for a starting model only including covariates 3 and 6.
If start.model is set to an integer (e.g. start.model=15) then that number of covariates (here: 15 covariates) is randomly chosen and the starting model is identified by those regressors with an OLS t-statistic>0.2.
The default value start.value=NA corresponds to start.value=min(ncol(X.data),nrow(X.data)-3). Note that start.value=0 or start.value=NULL starts from the null model.
If mcmc="enumerate" then start.value is the index to start the iteration (default: 0, the null model) . Any number between 0 and K^2-1 is admissible.

TRUE if statistics on the shrinkage factor g/(1+g) should be collected, defaulting to TRUE (Note: set g.stats=FALSE for faster iteration.)

setting logfile=TRUE produces a logfile named "test.log" in your current working directory, in order to keep track of the sampling procedure. logfile equal to some filepath (like logfile="subfolder/log.txt") puts the logfile into that specified position. (default: logfile=FALSE). Note that logfile="" implies log printouts on the console.

specifies at which number of posterior draws information is written to the log file; default: 10 000 iterations

default FALSE. If force.full.ols=TRUE, the OLS estimation part of the sampling procedure relies on slower matrix inversion, instead of streamlined routines. force.full.ols=TRUE can slow down sampling but may deal better with highly collinear data

indices or variable names of X.data that are fixed regressors to be always included in every sampled model. Note: the parameter mprior.size refers to prior model size including these fixed regressors.

a list of aggregate statistics: iter is the number of iterations, burn the number of burn-ins.
The following have to be divided by cumsumweights to get posterior expected values: inccount are the posterior inclusion probabilities, b1mo and b2mo the first and second moment of coefficients, add.otherstats other statistics of interest (typically the moments of the shrinkage factor), msize is the post. expected model size, k.vec the posterior model size distribution, pos.sign the unconditional post. probability of positive coefficients, corr.pmp is the correlation between the best models' MCMC frequencies and their marg. likelihoods.
timed is the time that was needed for MCMC sampling, cons is the posterior expected value of the constant. K and N are the maximum number of covariates and the sample size, respectively.

a list of the evaluated function arguments provided to bms (see above)

a 'topmod' object containing the best drawn models. see topmod for more details

the positions of the starting model. If bmao is a'bma' object this corresponds to covariates bmao$reg.names[bmao$start.pos]. If bmao is a chain that resulted from several starting models (cf. c.bma, then start.pos is a list detailing all of them.

a list of class gprior-class, detailing information on the g-prior: gtype corresponds to argument g above, is.constant is FALSE if gtype is either "hyper" or "EBL", return.g.stats corresponds to argument g.stats above, shrinkage.moments contains the first and second moments of the shrinkage factor (only if return.g.stats==TRUE), g details the fixed g (if is.constant==TRUE), hyper.parameter corresponds to the hyper-g parameter a as in Liang et al. (2008)

a list of class mprior-class, detailing information on the model prior: origargs lists the original arguments to mprior and mprior.size above; mp.msize denotes the prior mode size; mp.Kdist is a (K+1) vector with the prior model size distribution from 0 to K

data.frame or matrix: corresponds to argument X.data above, possibly cleaned for NAs

character vector: the covariate names to be used for X.data (corresponds to variable.names.bma

the original call to the bms function