trendtest.Gibbs.AR: Obtain Bayesian trend test and posterior distributions for...
In BayesSingleSub: Computation of Bayes factors for interrupted time-series designs
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
This function computes Bayes factors for the trend and intercept differences between two phases of a single subject data sequence,
using Gibbs sampling. Posterior samples of parameters are also provided.
Usage
1
2
3
4
5
6
7
Arguments
before
A vector of observations, in time order, taken in Phase 1 (e.g., before the treatment).
after
A vector of observations, in time order, taken in Phase 2 (e.g., after the treatment).
iterations
Number of Gibbs sampler iterations to perform.
intArea
Only used if return.chains=TRUE. Bounds for the interval null hypothesis for the intercept difference.
slpArea
Only used if return.chains=TRUE. Bounds for the interval null hypothesis for the trend difference.
leftSidedInt
Only used if return.onesided = TRUE. Should the one sided Bayes factor for the intercept difference be one sided?
leftSidedSlp
Only used if return.onesided = TRUE. Should the one sided Bayes factor for the trend difference be one sided?
r.scaleInt
Prior scale for the intercept difference (see Details below).
r.scaleSlp
Prior scale for the trend difference (see Details below).
alphaTheta
The alpha parameter of the beta prior on theta (see Details below).
betaTheta
The beta parameter of the beta prior on theta (see Details below).
sdMet
Scale for the Metropolis-Hastings sampling of theta (see Details below).
progress
Report progress with a text progress bar?
return.chains
Return posterior samples of parameters?.
return.onesided
Return one sided Bayes factors?
Details
This function computes Bayes factors for the differences in trend and intercept between two data sequences from a single subject,
using Gibbs sampling. The Bayes factor for trend difference compares the null hypothesis of no true trend difference against the
alternative hypothesis of a true trend difference. The Bayes factor for intercept difference compares the null hypothesis of no
true intercept difference against the alternative hypothesis of a true intercept difference. Also, a joined Bayes factor for the
trend and intercept combined is provided. Bayes factors larger than 1 support the null hypothesis, Bayes factors smaller than 1 support
the alternative hypothesis. Auto-correlation of the errors is modeled by a first order auto-regressive process.
Posterior distributions of the model parameters can also be obtained. Model parameters of interest include mu0 (overall mean),
sig*delta (difference between intercepts), beta0 (overall trend), sig*beta1 (difference between trends), sig2 (variance of the random
shocks), and rho (auto-correlation).
Cauchy priors are placed on the standardized trend and intercept differences. The r.scaleInt and r.scaleSlp arguments
control the scales of these Cauchy priors, with r.scaleInt = 1 and r.scaleSlp = 1 yielding standard Cauchy priors.
A noninformative Jeffreys prior is placed on the variance of the random shocks of the auto-regressive process. A beta prior is
placed on the auto-correlation theta. The alphaTheta and betaTheta arguments control the form of this beta prior.
Missing data are sampled from the likelihood function, conditioned at the observed data, at each iteration of the Gibbs sampler.
Value
A list containing the following:
logbf
MCMC estimates of the log two sided point null Bayes factors, computed using the Savage-Dickey method (Morey, Rouder, Pratte, and Speckman, submitted).
chains
Only returned if return.chains=TRUE. An object of type MCMC containing the chains for each parameter.
acc
Only returned if return.chains=TRUE. The Metropolis-Hastings acceptance rate.
logbfArea
Only returned if return.chains=TRUE. MCMC estimates of the log two sided interval null Bayes factors.
logbfOnesided
Only returned if return.onesided=TRUE. MCMC estimates of the log one sided point null Bayes factors.
Note
For a more accurate method of computing the Bayes factor, see trendtest.MC.AR.
Author(s)
Richard D. Morey and Rivka de Vries
References
De Vries, R. M. \& Morey, R. D. (submitted). Bayesian hypothesis testing Single-Subject Data. Psychological Methods.
R code guide: http://drsmorey.org/research/rdmorey/
See Also
trendtest.MC.AR, ttest.Gibbs.AR, ttest.MCGQ.AR
Examples
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18
## Define data
data = c(87.5, 82.5, 53.4, 72.3, 94.2, 96.6, 57.4, 78.1, 47.2,
80.7, 82.1, 73.7, 49.3, 79.3, 73.3, 57.3, 31.7, 50.4, 77.8,
67, 40.5, 1.6, 38.6, 3.2, 24.1)
## Obtain log Bayes factors
logBFs = trendtest.Gibbs.AR(data[1:10], data[11:25])
## Obtain log Bayes factors, chains, and log interval null Bayes factors
output = trendtest.Gibbs.AR(data[1:10], data[11:25],
return.chains = TRUE, intArea = c(-0.2,0.2),
slpArea = c(-0.2, 0.2))
## Look at the posterior distribution of the mean
plot(output$chains[,1])
## Obtain summary statistics of posterior distributions
summary(output$chains)
Example output
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rho acceptance rate: 0.3153153
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rho acceptance rate: 0.3153153
Iterations = 1:1000
Thinning interval = 1
Number of chains = 1
Sample size per chain = 1000
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
mu0 76.2327 8.9496 0.283010 0.30156
sig*delta 8.2158 13.6878 0.432847 0.43285
beta0 -2.4518 1.1545 0.036509 0.03651
sig*beta1 -3.2708 2.6657 0.084296 0.08179
sig2 346.6500 111.6138 3.529537 5.83900
g1 12.7221 216.6363 6.850641 6.85064
g2 5.6421 82.7235 2.615946 2.61595
rho 0.1277 0.1119 0.003538 0.01062
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
mu0 57.84865 70.87614 76.3184 81.5305 93.31316
sig*delta -17.44681 -0.64663 7.6457 16.8342 35.66630
beta0 -4.76458 -3.16681 -2.4553 -1.7659 -0.09218
sig*beta1 -8.76121 -4.89039 -3.3302 -1.5983 1.98036
sig2 199.16324 268.89154 322.5940 398.6094 632.04269
g1 0.16935 0.55290 1.1664 2.9099 30.91282
g2 0.14644 0.40099 0.7333 1.6430 18.34464
rho 0.00636 0.04428 0.1036 0.1757 0.42986
BayesSingleSub documentation built on May 2, 2019, 8:26 a.m.
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
This function computes Bayes factors for the trend and intercept differences between two phases of a single subject data sequence, using Gibbs sampling. Posterior samples of parameters are also provided.
Usage
1 2 3 4 5 6 7 |
Arguments
before |
A vector of observations, in time order, taken in Phase 1 (e.g., before the treatment). |
after |
A vector of observations, in time order, taken in Phase 2 (e.g., after the treatment). |
iterations |
Number of Gibbs sampler iterations to perform. |
intArea |
Only used if |
slpArea |
Only used if |
leftSidedInt |
Only used if |
leftSidedSlp |
Only used if |
r.scaleInt |
Prior scale for the intercept difference (see Details below). |
r.scaleSlp |
Prior scale for the trend difference (see Details below). |
alphaTheta |
The alpha parameter of the beta prior on theta (see Details below). |
betaTheta |
The beta parameter of the beta prior on theta (see Details below). |
sdMet |
Scale for the Metropolis-Hastings sampling of theta (see Details below). |
progress |
Report progress with a text progress bar? |
return.chains |
Return posterior samples of parameters?. |
return.onesided |
Return one sided Bayes factors? |
Details
This function computes Bayes factors for the differences in trend and intercept between two data sequences from a single subject, using Gibbs sampling. The Bayes factor for trend difference compares the null hypothesis of no true trend difference against the alternative hypothesis of a true trend difference. The Bayes factor for intercept difference compares the null hypothesis of no true intercept difference against the alternative hypothesis of a true intercept difference. Also, a joined Bayes factor for the trend and intercept combined is provided. Bayes factors larger than 1 support the null hypothesis, Bayes factors smaller than 1 support the alternative hypothesis. Auto-correlation of the errors is modeled by a first order auto-regressive process.
Posterior distributions of the model parameters can also be obtained. Model parameters of interest include mu0 (overall mean), sig*delta (difference between intercepts), beta0 (overall trend), sig*beta1 (difference between trends), sig2 (variance of the random shocks), and rho (auto-correlation).
Cauchy priors are placed on the standardized trend and intercept differences. The r.scaleInt and r.scaleSlp arguments
control the scales of these Cauchy priors, with r.scaleInt = 1 and r.scaleSlp = 1 yielding standard Cauchy priors.
A noninformative Jeffreys prior is placed on the variance of the random shocks of the auto-regressive process. A beta prior is
placed on the auto-correlation theta. The alphaTheta and betaTheta arguments control the form of this beta prior.
Missing data are sampled from the likelihood function, conditioned at the observed data, at each iteration of the Gibbs sampler.
Value
A list containing the following:
logbf |
MCMC estimates of the log two sided point null Bayes factors, computed using the Savage-Dickey method (Morey, Rouder, Pratte, and Speckman, submitted). |
chains |
Only returned if |
acc |
Only returned if |
logbfArea |
Only returned if |
logbfOnesided |
Only returned if |
Note
For a more accurate method of computing the Bayes factor, see trendtest.MC.AR.
Author(s)
Richard D. Morey and Rivka de Vries
References
De Vries, R. M. \& Morey, R. D. (submitted). Bayesian hypothesis testing Single-Subject Data. Psychological Methods.
R code guide: http://drsmorey.org/research/rdmorey/
See Also
trendtest.MC.AR, ttest.Gibbs.AR, ttest.MCGQ.AR
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ## Define data
data = c(87.5, 82.5, 53.4, 72.3, 94.2, 96.6, 57.4, 78.1, 47.2,
80.7, 82.1, 73.7, 49.3, 79.3, 73.3, 57.3, 31.7, 50.4, 77.8,
67, 40.5, 1.6, 38.6, 3.2, 24.1)
## Obtain log Bayes factors
logBFs = trendtest.Gibbs.AR(data[1:10], data[11:25])
## Obtain log Bayes factors, chains, and log interval null Bayes factors
output = trendtest.Gibbs.AR(data[1:10], data[11:25],
return.chains = TRUE, intArea = c(-0.2,0.2),
slpArea = c(-0.2, 0.2))
## Look at the posterior distribution of the mean
plot(output$chains[,1])
## Obtain summary statistics of posterior distributions
summary(output$chains)
|
Example output
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rho acceptance rate: 0.3153153
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rho acceptance rate: 0.3153153
Iterations = 1:1000
Thinning interval = 1
Number of chains = 1
Sample size per chain = 1000
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
mu0 76.2327 8.9496 0.283010 0.30156
sig*delta 8.2158 13.6878 0.432847 0.43285
beta0 -2.4518 1.1545 0.036509 0.03651
sig*beta1 -3.2708 2.6657 0.084296 0.08179
sig2 346.6500 111.6138 3.529537 5.83900
g1 12.7221 216.6363 6.850641 6.85064
g2 5.6421 82.7235 2.615946 2.61595
rho 0.1277 0.1119 0.003538 0.01062
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
mu0 57.84865 70.87614 76.3184 81.5305 93.31316
sig*delta -17.44681 -0.64663 7.6457 16.8342 35.66630
beta0 -4.76458 -3.16681 -2.4553 -1.7659 -0.09218
sig*beta1 -8.76121 -4.89039 -3.3302 -1.5983 1.98036
sig2 199.16324 268.89154 322.5940 398.6094 632.04269
g1 0.16935 0.55290 1.1664 2.9099 30.91282
g2 0.14644 0.40099 0.7333 1.6430 18.34464
rho 0.00636 0.04428 0.1036 0.1757 0.42986
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