This is an R-package to assess qualitative individual differences using Bayesian model comparison and estimation.
quid
uses Bayesian mixed models to estimate individual effect sizes
and to test theoretical order constraints in repeated measures designs.
It offers a method for testing the direction of individual effects.
Typical questions that can be answered with this package are of the
sort: “Does everyone show an effect in the same direction?” and “are
there qualitative individual differences?”.
This is a quick start guide. For an extensive description of the package and the statistical models used see the main manual.
At this point the quid
package can only be installed from github. For
this you need to install the devtools
package and then run the
install_github
function. You can include the argument
build_vignettes = TRUE
to also install this manual. This might take
slightly longer to install. Lastly, you have to load the package via
library
:
devtools::install_github("lukasklima/quid", build_vignettes = TRUE)
library(quid)
| Function | Description |
|:-----------------------|:------------------------------------------------------------------|
| constraintBF
| Main function to calculate Bayes factors for constraints |
| calculateDifferences
| Calculate differences between conditions specified in constraints |
| plotEffects
| Plot a BFBayesFactorConstraint object |
To impute constraints, use the whichConstraint
argument of the
constraintBF
function. whichConstraint
takes a named vector, where
the names are the name of the effect factor and the values are the
constraints on effect levels. For instance, say you have a column that
holds the condition (condition
) with levels treatment
and control
.
You want to check if the outcome variable (outcome
) is bigger in the
treatment condition, so your input should look like this:
whichConstraint = c("condition" = "treatment > control")
If you have a third (or more) level(s), say a low dose treatment
(low_dose
) and you want to test whether the effect in the treatment
condition is bigger than in the low dose condition and the effect in the
low dose condition is bigger than in the control condition your input
should look like this:
whichConstraint = c("condition" = "treatment > low_dose", "condition" = "low_dose > control")
In this example we use the stroop
data set, which is part of quid
.
See ?stroop
for details. We want to test whether the response time in
seconds (rtS
) is bigger in the incongruent (2
) condition than in
the congruent (1
) condition.
We use a formula to express the model. The outcome variable rtS
is
modelled as a function of the main effect of ID
(person variable), the
main effect of cond
(condition variable) and their interaction
(ID:cond
). In short, this can be expressed as ID*cond
.
The whichRandom
argument specifies that ID
is a random factor. The
ID
argument specifies that the participants’ IDs are stored in the
variable "ID"
. The rscaleEffects
argument is used to specify priors
for the fixed, random and interaction effect.
data(stroop)
resStroop <- constraintBF(formula = rtS ~ ID*cond,
data = stroop,
whichRandom = "ID",
ID = "ID",
whichConstraint = c("cond" = "2 > 1"),
rscaleEffects = c("ID" = 1, "cond" = 1/6, "ID:cond" = 1/10))
Printing the resStroop
object produces the following output:
resStroop
#>
#> Constraints analysis
#> --------------
#> Bayes factor : 12.46582
#> Posterior probability : 0.6584444
#> Prior probability : 0.05282
#>
#> Constraints defined:
#> cond : 1 < 2
#>
#> =========================
#>
#> Bayes factor analysis
#> --------------
#> [1] ID : 3.945904e+428 ±0%
#> [2] cond : 9.175351e+50 ±0%
#> [3] ID + cond : 4.491989e+490 ±0.89%
#> [4] ID + cond + ID:cond : 1.341518e+491 ±1.57%
#>
#> Against denominator:
#> Intercept only
#> ---
#> Bayes factor type: BFlinearModel, JZS
Under “Constraints analysis” you see the Bayes factor in favour of your
defined constraints, where the full model [4]
(under Bayes factor
analysis) is in the denominator. So, the Bayes factor of the
constraints analysis is the Bayes factor between the constrained model
and model [4]
. Furthermore, you can see the posterior and prior
probabilities of the constraints given the unconstrained model. You can
think of the prior probability as the probability of the constraints
holding before seeing the data, and the posterior probability as the
probability of the constraints holding after seeing the data. We see
that the constrained model is the preferred model.
Under “Bayes factor analysis” you can see the output from the
generalTestBF
function from the BayesFactor
package. See the
BayesFactor vignettes for details on how to manipulate Bayes factor
objects. Model number three [3]
with only main effects is the common
effect model. Model number four [4]
with the interaction term
ID:cond
allows for random slopes. The random effects model is the
preferred model which suggests that the equality constraint does not
hold. You can get a direct comparison between the two by manipulating
the generalTestObj
slot of the resStroop
object:
bfs <- resStroop@generalTestObj
bfs[4] / bfs[3]
#> Bayes factor analysis
#> --------------
#> [1] ID + cond + ID:cond : 2.986467 ±1.81%
#>
#> Against denominator:
#> rtS ~ ID + cond
#> ---
#> Bayes factor type: BFlinearModel, JZS
To get a comparison between the prefered model and all other models:
bfs / max(bfs)
#> Bayes factor analysis
#> --------------
#> [1] ID : 2.941373e-63 ±1.57%
#> [2] cond : 6.839531e-441 ±1.57%
#> [3] ID + cond : 0.3348438 ±1.81%
#> [4] ID + cond + ID:cond : 1 ±0%
#>
#> Against denominator:
#> rtS ~ ID + cond + ID:cond
#> ---
#> Bayes factor type: BFlinearModel, JZS
You can produce a plot of the individual effects; both the observed
effects and the model estimates. The individual effects are the
differences between the levels you specified in your constraints. In the
plot below, we see the individual differences in response times between
cond = 2
and cond = 1
.
plotEffects(resStroop)
We can see that the observed effects shows individuals with a negative effect. However, the model estimates are shrunk towards the grand mean and no individual has an estimated true negative effect.
If you want to manipulate the plot, you can do so by adding ggplot2
layers to it, or start from scratch by setting the .raw
argument to
TRUE
to get the data.frame
used to produce the plot.
plotEffects(resStroop, .raw = TRUE)
We conclude this quick start guide by showing how to impute more than
one constraint and how the output looks like. For this, we use the ld5
data set, which is part of quid
. See ?ld5
for details.
The plotting function produces a comparison of observed effects versus the model estimates for each difference defined in your constraints. On the right side of the plot you see the labels of the differences.
data(ld5)
resLD5 <- constraintBF(formula = rt ~ sub * distance + side,
data = ld5,
whichRandom = c("sub"),
ID = "sub",
whichConstraint = c("distance" = "1 > 2", "distance" = "2 > 3"),
rscaleEffects = c("sub" = 1,
"side" = 1/6,
"distance" = 1/6,
"sub:distance" = 1/10))
plotEffects(resLD5)
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.