Package 'mashr'

Create contrast matrix

Description

Create contrast matrix

Usage

contrast_matrix(R, ref, name = 1:R)

Arguments

R	the number of column for the contrast matrix
ref	the reference group. It could be a number between 1,..., R, R is number of conditions, or the name of reference group. If there is no reference group, it can be the string 'mean'.
name	a length R vector contains the name for conditions

Examples

contrast_matrix(5, 'mean')

---

Compute a list of canonical covariance matrices

Description

Compute a list of canonical covariance matrices

Usage

cov_canonical(
  data,
  cov_methods = c("identity", "singletons", "equal_effects", "simple_het")
)

Arguments

data

a mash data object, eg as created by mash_set_data

cov_methods

a vector of strings indicating the matrices to be used: "identity" for the identity (effects are independent among conditions); "singletons" for the set of matrices with just one non-zero entry $x_{jj} = 1, j = 1,...,R$; (effect specific to condition j); "equal_effects" for the matrix of all 1s (effects are equal among conditions); "simple_het" for a set of matrices with 1s on the diagonal and all off-diagonal elements equal to 0.25, 0.5 or 0.75; see cov_simple_het for details; (effects are correlated among conditions).

Details

The default is that this function computes covariance matrices corresponding to the "bmalite" models.

Value

a list of covariance matrices

Examples

data = mash_set_data(Bhat = cbind(c(1,2),c(3,4)), Shat = cbind(c(1,1),c(1,1)))
 cov_canonical(data)
 cov_canonical(data,"singletons")
 cov_canonical(data,c("id","sing")) # can use partial matching of names

---

Perform "extreme deconvolution" (Bovy et al) on a subset of the data

Description

Perform "extreme deconvolution" (Bovy et al) on a subset of the data

Usage

cov_ed(data, Ulist_init, subset = NULL, algorithm = c("bovy", "teem"), ...)

Arguments

data	a mash data object
Ulist_init	a named list of covariance matrices to use to initialize ED; default is to use matrices from PCs
subset	a subset of data to be used when ED is run (set to NULL for all the data)
algorithm	algorithm to run ED
...	other arguments to be passed to ED algorith, see extreme_deconvolution for algorithm 'bovy', or teem_wrapper for algorithm 'teem'

Details

Runs the extreme deconvolution algorithm from Bovy et al (Annals of Applied Statistics) to estimate data-driven covariance matrices. It can be initialized with, for example running cov_pca with, say, 5 PCs.

Examples

## Not run: 
data = mash_set_data(Bhat = cbind(c(1,2),c(3,4)), Shat = cbind(c(1,1),c(1,1)))
U_pca = cov_pca(data,2)
U_x = apply(data$Bhat, 2, function(x) x - mean(x))
U_xx = t(U_x) %*% U_x / nrow(U_x)
cov_ed(data,c(U_pca, list(xx = U_xx)))

## End(Not run)

---

Perform Empirical Bayes Matrix Factorization using flashier, and return a list of candidate covariance matrices

Description

Perform Empirical Bayes Matrix Factorization using flashier, and return a list of candidate covariance matrices

Usage

cov_flash(
  data,
  factors = c("default", "nonneg"),
  subset = NULL,
  remove_singleton = FALSE,
  tag = NULL,
  output_model = NULL,
  greedy_args = list(),
  backfit_args = list()
)

Arguments

data	A “mash” data object.
factors	If factors = "default", the factors and loadings are both unconstrained. If factors = "nonneg", the factors are constrained to be non-negative, and the loadings are unconstrained.
subset	Data samples (rows) used to estimate the covariances. Sset to NULL to use all the data.
remove_singleton	If remove_singleton = TRUE, factors corresponding to singleton matrices will be removed from the output.
tag	How to name the covariance matrices.
output_model	The fitted flash model will be saved to this file (using saveRDS).
greedy_args	List containing additional parameters passed to flashier::flash_greedy.
backfit_args	List containing additional parameters passed to flashier::flash_backfit.

Value

A list of covariance matrices.

Examples

# See https://stephenslab.github.io/mashr/articles/flash_mash.html
# for an example

---

Perform PCA on data and return list of candidate covariance matrices

Description

Perform PCA on data and return list of candidate covariance matrices

Usage

cov_pca(data, npc, subset = NULL)

Arguments

data	a mash data object
npc	the number of PCs to use
subset	indices of the subset of data to use (set to NULL for all data)

Value

Returns a list of covariance matrices: the npc rank-one covariance matrices based on the first npc PCs, and the rank npc covariance matrix. If flashier did not identify any factors, NULL is returned.

Examples

data = mash_set_data(Bhat = cbind(c(1,2),c(3,4)), Shat = cbind(c(1,1),c(1,1)))
cov_pca(data,2)

---

Compute a list of covariance matrices corresponding to the "Unassociated", "Directly associated" and "Indirectly associated" models

Description

Compute a list of covariance matrices corresponding to the "Unassociated", "Directly associated" and "Indirectly associated" models

Usage

cov_udi(data, model = udi_model_matrix(n_conditions(data)))

Arguments

data	a mash data object, eg as created by mash_set_data
model	a model matrix with R columns, where R is the number of conditions in the data; each row should be a vector of length R with elements "U","D" and "I" indicating whether each effect is Unassociated, Directly associated or Indirectly associated

Details

If model is specified then this returns the covariance matrices for those models. The default creates all possible models. For a desription of the "Unassociated", "Directly associated" and "Indirectly associated" models see Stephens M (2013), A unified framework for Association Analysis with Multiple Related Phenotypes, PloS ONE.

Value

a named list of covariance matrices

Examples

data = mash_set_data(Bhat = cbind(c(1,2),c(3,4)), Shat = cbind(c(1,1),c(1,1)))
cov_udi(data)
cov_udi(data,c('I','D'))

---

Estimate null correlations (simple)

Description

Estimates a null correlation matrix from data using simple z score threshold

Usage

estimate_null_correlation_simple(data, z_thresh = 2, est_cor = TRUE)

Arguments

data	a mash data object, eg as created by mash_set_data
z_thresh	the z score threshold below which to call an effect null
est_cor	whether to estimate correlation matrix (TRUE) or the covariance matrix (FALSE).

Details

Returns a simple estimate of the correlation matrix (or covariance matrix) among conditions under the null. Specifically, the simple estimate is the empirical correlation (or covariance) matrix of the z scores for those effects that have (absolute) z score < z_thresh in all conditions.

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
estimate_null_correlation_simple(data)

---

Density estimation using Gaussian mixtures in the presence of noisy, heterogeneous and incomplete data

Description

We present a general algorithm to infer a d-dimensional distribution function given a set of heterogeneous, noisy observations or samples. This algorithm reconstructs the error-deconvolved or 'underlying' distribution function common to all samples, even when the individual samples have unique error and missing-data properties. The underlying distribution is modeled as a mixture of Gaussians, which is completely general. Model parameters are chosen to optimize a justified, scalar objective function: the logarithm of the probability of the data under the error-convolved model, where the error convolution is different for each data point. Optimization is performed by an Expectation Maximization (EM) algorithm, extended by a regularization technique and 'split-and-merge' procedure. These extensions mitigate problems with singularities and local maxima, which are often encountered when using the EM algorithm to estimate Gaussian density mixtures.

Usage

extreme_deconvolution(
  ydata,
  ycovar,
  xamp,
  xmean,
  xcovar,
  projection = NULL,
  weight = NULL,
  fixamp = NULL,
  fixmean = NULL,
  fixcovar = NULL,
  tol = 1e-06,
  maxiter = 1e+09,
  w = 0,
  logfile = NULL,
  splitnmerge = 0,
  maxsnm = FALSE,
  likeonly = FALSE,
  logweight = FALSE
)

Arguments

ydata	[ndata,dy] matrix of observed quantities
ycovar	[ndata,dy] / [ndata,dy,dy] / [dy,dy,ndata] matrix, list or 3D array of observational error covariances (if [ndata,dy] then the error correlations are assumed to vanish)
xamp	[ngauss] array of initial amplitudes (*not* [1,ngauss])
xmean	[ngauss,dx] matrix of initial means
xcovar	[ngauss,dx,dx] list of matrices of initial covariances
projection	[ndata,dy,dx] list of projection matrices
weight	[ndata] array of weights to be applied to the data points
fixamp	(default=None) None, True/False, or list of bools
fixmean	(default=None) None, True/False, or list of bools
fixcovar	(default=None) None, True/False, or list of bools
tol	(double, default=1.e-6) tolerance for convergence
maxiter	(long, default= 10**9) maximum number of iterations to perform
w	(double, default=0.) covariance regularization parameter (of the conjugate prior)
logfile	basename for several logfiles (_c.log has output from the c-routine; _loglike.log has the log likelihood path of all the accepted routes, i.e. only parts which increase the likelihood are included, during splitnmerge)
splitnmerge	(int, default=0) depth to go down the splitnmerge path
maxsnm	(Bool, default=False) use the maximum number of split 'n' merge steps, K*(K-1)*(K-2)/2
likeonly	(Bool, default=False) only compute the total log likelihood of the data
logweight	(bool, default=False) if True, weight is actually log(weight)

Value

avgloglikedata	avgloglikedata after convergence
xamp	updated xamp
xmean	updated xmean
xcovar	updated xcovar

Author(s)

Jo Bovy, David W. Hogg, & Sam T. Roweis

References

Inferring complete distribution functions from noisy, heterogeneous and incomplete observations Jo Bovy, David W. Hogg, & Sam T. Roweis, Submitted to AOAS (2009) [arXiv/0905.2979]

Examples

## Not run: 
ydata <-
c(2.62434536, 0.38824359, 0.47182825, -0.07296862, 1.86540763,
  -1.30153870, 2.74481176, 0.23879310, 1.31903910, 0.75062962,
  2.46210794, -1.06014071, 0.67758280, 0.61594565, 2.13376944,
  -0.09989127, 0.82757179, 0.12214158, 1.04221375, 1.58281521,
  -0.10061918, 2.14472371, 1.90159072, 1.50249434, 1.90085595,
  0.31627214, 0.87710977, 0.06423057, 0.73211192, 1.53035547,
  0.30833925, 0.60324647, 0.31282730, 0.15479436, 0.32875387,
  0.98733540, -0.11731035, 1.23441570, 2.65980218, 1.74204416,
  0.80816445, 0.11237104, 0.25284171, 2.69245460, 1.05080775,
  0.36300435, 1.19091548, 3.10025514, 1.12015895, 1.61720311,
  1.30017032, 0.64775015, -0.14251820, 0.65065728, 0.79110577,
  1.58662319, 1.83898341, 1.93110208, 1.28558733, 1.88514116,
  0.24560206, 2.25286816, 1.51292982, 0.70190717, 1.48851815,
  0.92442829, 2.13162939, 2.51981682, 3.18557541, -0.39649633,
  -0.44411380, 0.49553414, 1.16003707, 1.87616892, 1.31563495,
  -1.02220122, 0.69379599, 1.82797464, 1.23009474, 1.76201118,
  0.77767186, 0.79924193, 1.18656139, 1.41005165, 1.19829972,
  1.11900865, 0.32933771, 1.37756379, 1.12182127, 2.12948391,
  2.19891788, 1.18515642, 0.62471505, 0.36126959, 1.42349435,
  1.07734007, 0.65614632, 1.04359686, 0.37999916, 1.69803203,
  0.55287144, 2.22450770, 1.40349164, 1.59357852, -0.09491185,
  1.16938243, 1.74055645, 0.04629940, 0.73378149, 1.03261455,
  -0.37311732, 1.31515939, 1.84616065, 0.14048406, 1.35054598,
  -0.31228341, 0.96130449, -0.61577236, 2.12141771, 1.40890054,
  0.97538304, 0.22483838, 2.27375593, 2.96710175, -0.85798186,
  2.23616403, 2.62765075, 1.33801170, -0.19926803, 1.86334532,
  0.81907970, 0.39607937, -0.23005814, 1.55053750, 1.79280687,
  0.37646927, 1.52057634, -0.14434139, 1.80186103, 1.04656730,
  0.81343023, 0.89825413, 1.86888616, 1.75041164, 1.52946532,
  1.13770121, 1.07782113, 1.61838026, 1.23249456, 1.68255141,
  0.68988323, -1.43483776, 2.03882460, 3.18697965, 1.44136444,
  0.89984477, 0.86355526, 0.88094581, 1.01740941, -0.12201873,
  0.48290554, 0.00297317, 1.24879916, 0.70335885, 1.49521132,
  0.82529684, 1.98633519, 1.21353390, 3.19069973, -0.89636092,
  0.35308331, 1.90148689, 3.52832571, 0.75136522, 1.04366899,
  0.77368576, 2.33145711, 0.71269214, 1.68006984, 0.68019840,
  -0.27255875, 1.31354772, 1.50318481, 2.29322588, 0.88955297,
  0.38263794, 1.56276110, 1.24073709, 1.28066508, 0.92688730,
  2.16033857, 1.36949272, 2.90465871, 2.11105670, 1.65904980,
  -0.62743834, 1.60231928, 1.42028220, 1.81095167, 2.04444209)

ydata  <- matrix(ydata,length(ydata),1)
N      <- dim(ydata)[1]
ycovar <- ydata*0 + 0.01
xamp   <- c(0.5,0.5)
xmean  <- matrix(c(0.86447943, 0.67078879, 0.322681, 0.45087394),2,2)
xcovar <-
  list(matrix(c(0.03821028, 0.04014796, 0.04108113, 0.03173839),2,2),
       matrix(c(0.06219194, 0.09738021, 0.04302473, 0.06778009),2,2))
projection <- list()
for (i in 1:N)
  projection[[i]] = matrix(c(i%%2,(i+1)%%2),1,2)
res <- extreme_deconvolution(ydata, ycovar, xamp, xmean, xcovar,
         projection=projection, logfile="ExDeconDemo")

## End(Not run)

---

Return the estimated mixture proportions

Description

Return the estimated mixture proportions

Usage

get_estimated_pi(m, dimension = c("cov", "grid", "all"))

Arguments

m	the mash result
dimension	indicates whether you want the mixture proportions for the covariances, grid, or all

Details

If the fit was done with 'usepointmass=TRUE' then the first element of the returned vector will correspond to the null, and the remaining elements to the non-null covariance matrices. Suppose the fit was done with $K$ covariances and a grid of length $L$. If 'dimension=cov' then the returned vector will be of length $K$ (or $K+1$ if 'usepointmass=TRUE'). If 'dimension=grid' then the returned vector will be of length $L$ (or $L+1$). If 'dimension=all' then the returned vector will be of length $LK$ (or $LK+1$). The names of the vector will be informative for which combination each element corresponds to.

Value

a named vector containing the estimated mixture proportions.

---

Return the Bayes Factor for each effect

Description

Return the Bayes Factor for each effect

Usage

get_log10bf(m)

Arguments

m	the mash result (from joint or 1by1 analysis); must have been computed using usepointmass=TRUE

Value

if m was fitted using usepointmass=TRUE then returns a vector of the log10(bf) values for each effect. That is, the jth element lbf[j] is log10(Pr(Bj | g=ghat-nonnull)/Pr(Bj | g = 0)) where ghat-nonnull is the non-null part of ghat. Otherwise returns NULL.

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
m = mash(data, cov_canonical(data))
get_log10bf(m)

---

Count number of conditions each effect is significant in

Description

Count number of conditions each effect is significant in

Usage

get_n_significant_conditions(
  m,
  thresh = 0.05,
  conditions = NULL,
  sig_fn = get_lfsr
)

Arguments

m	the mash result (from joint or 1by1 analysis)
thresh	indicates the threshold below which to call signals significant
conditions	which conditions to include in check (default to all)
sig_fn	the significance function used to extract significance from mash object; eg could be ashr::get_lfsr or ashr::get_lfdr

Value

a vector containing the number of significant conditions

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
m = mash(data, cov_canonical(data))
get_n_significant_conditions(m)

---

Compute the proportion of (significant) signals shared by magnitude in each pair of conditions, based on the poterior mean

Description

Compute the proportion of (significant) signals shared by magnitude in each pair of conditions, based on the poterior mean

Usage

get_pairwise_sharing(m, factor = 0.5, lfsr_thresh = 0.05, FUN = identity)

Arguments

m	the mash fit
factor	a number in [0,1] the factor within which effects are considered to be shared
lfsr_thresh	the lfsr threshold for including an effect in the assessment
FUN	a function to be applied to the estimated effect sizes before assessing sharing. The most obvious choice beside the default 'FUN=identity' would be 'FUN=abs' if you want to ignore the sign of the effects when assesing sharing.

Details

For each pair of tissues, first identify the effects that are significant (by lfsr<lfsr_thresh) in at least one of the two tissues. Then compute what fraction of these have an estimated (posterior mean) effect size within a factor 'factor' of one another. The results are returned as an R by R matrix.

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
m = mash(data, cov_canonical(data))
get_pairwise_sharing(m) # sharing by magnitude (same sign)
get_pairwise_sharing(m, factor=0) # sharing by sign
get_pairwise_sharing(m, FUN=abs) # sharing by magnitude when sign is ignored

---

Compute the proportion of (significant) signals shared by magnitude in each pair of conditions

Description

Compute the proportion of (significant) signals shared by magnitude in each pair of conditions

Usage

get_pairwise_sharing_from_samples(
  m,
  factor = 0.5,
  lfsr_thresh = 0.05,
  FUN = identity
)

Arguments

m	the mash fit with samples from posteriors
factor	a number in [0,1] the factor within which effects are considered to be shared
lfsr_thresh	the lfsr threshold for including an effect in the assessment
FUN	a function to be applied to the estimated effect sizes before assessing sharing. The most obvious choice beside the default 'FUN=identity' would be 'FUN=abs' if you want to ignore the sign of the effects when assesing sharing.

Details

For each pair of conditions, compute the fraction of effects that are within a factor 'factor' of one another. The results are returned as an R by R matrix.

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
m = mash(data, cov_canonical(data), posterior_samples=5, algorithm='R')
get_pairwise_sharing_from_samples(m) # sharing by magnitude (same sign)
get_pairwise_sharing_from_samples(m, factor=0) # sharing by sign
get_pairwise_sharing_from_samples(m, FUN=abs) # sharing by magnitude when sign is ignored

---

Condition-wise Posterior Summary

Description

Provide condition-wise summary based on posterior distributions for each effect.

Usage

get_posterior_condition_wise_summary(mash_data, m, contrast_mat)

Arguments

mash_data	A mash data object, e.g. as created by mash_set_data
m	A mash fit, typically an output from mash.
contrast_mat	A matrix applied to mashr fitting result, enabling comparisons for different conditions based on posteior distributions.

Value

See compute_posterior_matrices_common_cov_R.

Examples

# The following example performs pairwise comparisons in a data set
# with 5 conditions: that is, it compares conditions (column) 1 and
# 2, 1 and 3, 1 and 4, 1 and 5, 2 and 3, etc.
library(Matrix)
set.seed(1)
simdata <- simple_sims(100,5,1)
dat <- mash_set_data(simdata$Bhat,simdata$Shat)
U <- cov_canonical(dat)
m <- mash(dat,U)
x <- combn(5,2)
n <- ncol(x)
contrast_mat <- as.matrix(sparseMatrix(i = rep(1:n,each = 2),
                                       j = as.vector(x),
                                       x = 1,dims = c(n,5)))
res <- get_posterior_condition_wise_summary(dat,m,contrast_mat)

---

Return samples from a mash object

Description

Return samples from a mash object

Usage

get_samples(m)

Arguments

m	The mash fit.

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
m = mash(data, cov_canonical(data), posterior_samples=5, algorithm='R')
get_samples(m)

---

Find effects that are significant in at least one condition

Description

Find effects that are significant in at least one condition

Usage

get_significant_results(m, thresh = 0.05, conditions = NULL, sig_fn = get_lfsr)

Arguments

m	the mash result (from joint or 1by1 analysis)
thresh	indicates the threshold below which to call signals significant
conditions	which conditions to include in check (default to all)
sig_fn	the significance function used to extract significance from mash object; eg could be ashr::get_lfsr or ashr::get_lfdr. (Small values must indicate significant.)

Value

a vector containing the indices of the significant effects, by order of most significant to least

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
m = mash(data, cov_canonical(data))
get_significant_results(m)

---

Apply mash method to data

Description

Apply mash method to data

Usage

mash(
  data,
  Ulist = NULL,
  gridmult = sqrt(2),
  grid = NULL,
  normalizeU = TRUE,
  usepointmass = TRUE,
  g = NULL,
  fixg = FALSE,
  prior = c("nullbiased", "uniform"),
  nullweight = 10,
  optmethod = c("mixSQP", "mixIP", "mixEM", "cxxMixSquarem"),
  control = list(),
  verbose = TRUE,
  add.mem.profile = FALSE,
  algorithm.version = c("Rcpp", "R"),
  pi_thresh = 1e-10,
  A = NULL,
  posterior_samples = 0,
  seed = 123,
  outputlevel = 2,
  output_lfdr = FALSE
)

Arguments

data	a mash data object containing the Bhat matrix, standard errors, alpha value; created using mash_set_data or mash_set_data_contrast
Ulist	a list of covariance matrices to use (see normalizeU for rescaling these matrices)
gridmult	scalar indicating factor by which adjacent grid values should differ; close to 1 for fine grid
grid	vector of grid values to use (scaling factors omega in paper)
normalizeU	whether or not to normalize the U covariances to have maximum of 1 on diagonal
usepointmass	whether to include a point mass at 0, corresponding to null in every condition
g	the value of g obtained from a previous mash fit - an alternative to supplying Ulist, grid and usepointmass
fixg	if g is supplied, allows the mixture proportions to be fixed rather than estimated; e.g., useful for fitting mash to test data after fitting it to training data
prior	indicates what penalty to use on the likelihood, if any
nullweight	scalar, the weight put on the prior under “nullbiased” specification, see “prior”.
optmethod	name of optimization method to use
control	A list of control parameters passed to optmethod.
verbose	If TRUE, print progress to R console.
add.mem.profile	If TRUE, print memory usage to R console (requires R library 'profmem').
algorithm.version	Indicates whether to use R or Rcpp version
pi_thresh	threshold below which mixture components are ignored in computing posterior summaries (to speed calculations by ignoring negligible components)
A	the linear transformation matrix, Q x R matrix. This is used to compute the posterior for Ab.
posterior_samples	the number of samples to be drawn from the posterior distribution of each effect.
seed	A random number seed to use when sampling from the posteriors. It is used when posterior_samples > 0.
outputlevel	controls amount of computation / output; 1: output only estimated mixture component proportions, 2: and posterior estimates, 3: and posterior covariance matrices, 4: and likelihood matrices
output_lfdr	If output_lfdr = TRUE, output local false discovery rate estimates. The lfdr tends to be sensitive to mis-estimated covariance matrices, and generally we do not recommend using them; we recommend using the local false sign rate (lfsr) instead, which is always returned, even when output_lfdr = TRUE.

Value

a list with elements result, loglik and fitted_g

Examples

Bhat     = matrix(rnorm(100),ncol=5) # create some simulated data
Shat     = matrix(rep(1,100),ncol=5)
data     = mash_set_data(Bhat,Shat, alpha=1)
U.c      = cov_canonical(data)
res.mash = mash(data,U.c)

# Run mash with penalty exponent on null term equal to 100.
# See "False disovery rates: a new deal" (M. Stephens 2017),
# supplementary material S.2.5 for more details.
set.seed(1)
simdata = simple_sims(500,5,1)
data    = mash_set_data(simdata$Bhat,simdata$Shat)
U.c     = cov_canonical(data)
res0    = mash(data,U.c)
res1    = mash(data,U.c,prior = "nullbiased",nullweight = 101)
plot(res0$fitted_g$pi,res1$fitted_g$pi,pch = 20)
abline(a = 0,b = 1,col = "skyblue",lty = "dashed")

---

Perform condition-by-condition analyses

Description

Performs simple "condition-by-condition" analysis by running ash from package ashr on data from each condition, one at a time. May be a useful first step to identify top hits in each condition before a mash analysis.

Usage

mash_1by1(data, alpha = 0, ...)

Arguments

data	A list with the following two elements: Bhat an n by R matrix of observations (n units in R conditions); and Shat, an n by R matrix of standard errors (n units in R conditions),
alpha	Numeric value of alpha parameter in the model. alpha = 0 for Exchangeable Effects (EE), alpha = 1 for Exchangeable Z-scores (EZ).
...	optionally, other parameters to be passed to ash

Value

A list similar to the output of mash, particularly including posterior matrices.

Examples

simdata = simple_sims(50,5,1)
mash_1by1(simdata)

---

Compute loglikelihood for fitted mash object on new data.

Description

Compute loglikelihood for fitted mash object on new data.

Usage

mash_compute_loglik(g, data, algorithm.version = c("Rcpp", "R"))

Arguments

g	A mash object or the fitted_g from a mash object.
data	A set of data on which to compute the loglikelihood.
algorithm.version	Indicate R or Rcpp version

Details

The log-likelihood for each element is $p(Bhat_j | Shat_j,g,\alpha)$ where $Bhat_j | B_j, Shat_j \sim N(B_j, Shat_j)$ and $B_j/Shat_j^\alpha | Shat_j \sim g$.

Value

The log-likelihood for data computed using g.

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
m = mash(data, cov_canonical(data))
mash_compute_loglik(m,data)

---

Compute posterior matrices for fitted mash object on new data

Description

Compute posterior matrices for fitted mash object on new data

Usage

mash_compute_posterior_matrices(
  g,
  data,
  pi_thresh = 1e-10,
  algorithm.version = c("Rcpp", "R"),
  A = NULL,
  output_posterior_cov = FALSE,
  posterior_samples = 0,
  seed = 123
)

Arguments

g	a mash object or the fitted_g from a mash object.
data	a set of data on which to compute the posterior matrices
pi_thresh	threshold below which mixture components are ignored in computing posterior summaries (to speed calculations by ignoring negligible components)
algorithm.version	Indicates whether to use R or Rcpp version
A	the linear transformation matrix, Q x R matrix. This is used to compute the posterior for Ab.
output_posterior_cov	whether or not to output posterior covariance matrices for all effects
posterior_samples	the number of samples to be drawn from the posterior distribution of each effect.
seed	a random number seed to use when sampling from the posteriors. It is used when posterior_samples > 0.

Value

A list of posterior matrices

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
m = mash(data, cov_canonical(data))
mash_compute_posterior_matrices(m,data)

---

Compute vector of loglikelihood for fitted mash object on new data

Description

Compute vector of loglikelihood for fitted mash object on new data

Usage

mash_compute_vloglik(g, data, algorithm.version = c("Rcpp", "R"))

Arguments

g	A mash object.
data	A set of data on which to compute the loglikelihood.
algorithm.version	Indicate R or Rcpp version

Details

The log-likelihood for each element is $p(Bhat_j | Shat_j,g,\alpha)$ where $Bhat_j | B_j, Shat_j \sim N(B_j, Shat_j)$ and $B_j/Shat_j^\alpha | Shat_j \sim g$ Here the value of $\alpha$ is set when setting up the data object in 'mash_set_data'. If g is a mash object (safest!) then the function will check that this value matches the $\alpha$ used when fitting 'mash'. Note: as a convenience, this function can also be called with g a mixture distribution with same structure as the fitted_g from a mash object. This is mostly useful when doing simulations, where you might want to compute the likelihood under the "true" g. When used in this way the user is responsible for making sure that the g makes sense with the alpha set in data.

Value

The vector of log-likelihoods for each data point computed using g.

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
m = mash(data, cov_canonical(data))
mash_compute_vloglik(m,data)

---

Fit mash model and estimate residual correlations using EM algorithm

Description

Estimates a residual correlation matrix from data using an ad hoc EM algorithm.

Usage

mash_estimate_corr_em(
  data,
  Ulist,
  init,
  max_iter = 30,
  tol = 1,
  est_cor = TRUE,
  track_fit = FALSE,
  prior = c("nullbiased", "uniform"),
  details = TRUE,
  ...
)

Arguments

data	a mash data object, eg as created by mash_set_data
Ulist	a list of covariance matrices to use
init	the initial value for the residual correlation. If it is not given, we use result from estimate_null_correlation_simple
max_iter	maximum number of iterations to perform
tol	convergence tolerance
est_cor	whether to estimate correlation matrix (TRUE) or the covariance matrix (FALSE)
track_fit	add an attribute trace to output that saves current values of all iterations
prior	indicates what penalty to use on the likelihood, if any
details	whether to return details of the model, if it is TRUE, the mash model, the number of iterations and the value of objective functions will be returned
...	other parameters pass to mash

Details

Returns the estimated residual correlation matrix among conditions. We estimate the residual correlation matrix using an ad hoc em algorithm. The update in the ad hoc M step is not guaranteed to increase the likelihood, therefore, the EM algorithm is stopped before the likelihood drops. The residual correlation matrix V is estimated using the posterior second moment of the noise.

Warning: This method could take some time. The estimate_null_correlation_simple gives a quick approximation for the null correlation matrix.

Value

the estimated correlation matrix and the fitted mash model

V	estimated residual correlation matrix
mash.model	fitted mash model

Examples

simdata = simple_sims(100,5,1)
m.1by1 = mash_1by1(mash_set_data(simdata$Bhat,simdata$Shat))
strong.subset = get_significant_results(m.1by1,0.05)
random.subset = sample(1:nrow(simdata$Bhat),20)
data.strong = mash_set_data(simdata$Bhat[strong.subset,], simdata$Shat[strong.subset,])
data.tmp = mash_set_data(simdata$Bhat[random.subset,], simdata$Shat[random.subset,])
U_pca = cov_pca(data.strong, 3)
U_ed = cov_ed(data.strong, U_pca)
Vhat = mash_estimate_corr_em(data.tmp, U_ed)

---

Plot metaplot for an effect based on posterior from mash

Description

Plot metaplot for an effect based on posterior from mash

Usage

mash_plot_meta(m, i, xlab = "Effect size", ylab = "Condition", ...)

Arguments

m	the result of a mash fit
i	index of the effect to plot
xlab	Character string specifying x-axis label.
ylab	Character string specifying y-axis label.
...	Additional arguments passed to metaplot.

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
m = mash(data, cov_canonical(data))
mash_plot_meta(m,1)

---

Create a data object for mash analysis.

Description

Create a data object for mash analysis.

Usage

mash_set_data(
  Bhat,
  Shat = NULL,
  alpha = 0,
  df = Inf,
  pval = NULL,
  V = diag(ncol(Bhat)),
  zero_check_tol = .Machine$double.eps,
  zero_Bhat_Shat_reset = 0,
  zero_Shat_reset = 0
)

Arguments

Bhat	An N by R matrix of observed estimates.
Shat	An N by R matrix of corresponding standard errors. Shat can be a scalar if all standard errors are equal. This is most useful if Bhat is a matrix of Z scores, so elements of Shat are all 1. Default is 1.
alpha	Numeric value of alpha parameter in the model. alpha = 0 for Exchangeable Effects (EE), alpha = 1 for Exchangeable Z-scores (EZ). Default is 0. Please refer to equation (3.2) of M. Stephens 2016, Biostatistics for a discussion on alpha.
df	An N by R matrix of corresponding degrees of freedom of the t-statistic Bhat/Shat. Can be a scalar if all degrees of freedom are equal. Default is inf (for large samples).
pval	An N by R matrix of p-values of t-statistic Bhat/Shat. Shat and df should not be specified when pval is provided.
V	an R by R matrix / [R x R x N] array of effect specific correlation matrix of error correlations; must be positive definite. [So Bhat_j distributed as N(B_j,diag(Shat_j) V[,,j] diag(Shat_j)) where _j denotes the jth row of a matrix]. Defaults to identity.
zero_check_tol	a small positive number as threshold for Shat to be considered zero if any Shat is smaller or equal to this number.
zero_Bhat_Shat_reset	Replace zeros in Shat matrix to given value if the corresponding Bhat are also zeros.
zero_Shat_reset	Replace zeros in Shat matrix to given value.

Value

A data object for passing into mash functions.

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)

---

Update the data object for mash analysis.

Description

This function can update two parts of the mash data. The first one is setting the reference group, so the mash data can be used for commonbaseline analysis. The other one is updating the null correlation matrix.

Usage

mash_update_data(mashdata, ref = NULL, V = NULL)

Arguments

mashdata	mash data object ontaining the Bhat matrix, standard errors, V; created using mash_set_data
ref	the reference group. It could be a number between 1,..., R, R is number of conditions, or the name of reference group. If there is no reference group, it can be the string 'mean'.
V	an R by R matrix / [R x R x N] array of correlation matrix of error correlations

Value

a updated mash data object

Examples

simdata = simple_sims(50,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
mash_update_data(data, 'mean')

---

Create simplest simulation, cj = mu 1 data used for contrast analysis

Description

Create simplest simulation, cj = mu 1 data used for contrast analysis

Usage

sim_contrast1(nsamp = 100, ncond = 5, err_sd = sqrt(0.5))

Arguments

nsamp	number of samples of each type
ncond	number of conditions
err_sd	the standard deviation of the errors

Details

There is no true deviation exists in this case

Examples

sim_contrast1(100,5)

---

Create simulation with signal data used for contrast analysis.

Description

Create simulation with signal data used for contrast analysis.

Usage

sim_contrast2(nsamp = 1000, ncond = 5, err_sd = sqrt(0.5))

Arguments

nsamp	Number of samples of each type.
ncond	Number of conditions.
err_sd	The standard deviation of the errors.

Details

The first condition is the reference group. The deviations are the difference between the subsequent conditions with the reference group. The simulation consists of 90 10 different types of deviations: equal among conditions, present only in the first subsequent condition, independent across conditions.

Examples

sim_contrast2(100,5)

---

Create some simple simulated data for testing purposes

Description

Create some simple simulated data for testing purposes

Usage

simple_sims(nsamp = 100, ncond = 5, err_sd = 0.01)

Arguments

nsamp	number of samples of each type
ncond	number of conditions
err_sd	the standard deviation of the errors

Details

The simulation consists of equal numbers of four different types of effects: null, equal among conditions, present only in first condition, independent across conditions

Examples

simple_sims(100, 5)

---

Create some more simple simulated data for testing purposes

Description

Create some more simple simulated data for testing purposes

Usage

simple_sims2(nsamp = 100, err_sd = 0.01)

Arguments

nsamp	number of samples of each type
err_sd	the standard deviation of the errors

Details

The simulation consists of five conditions with two types of effecc those present (and identical) in first two conditions and those present (and identical) in last three conditions

Examples

simple_sims2(100, 5)

---