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
:
::install_github("lukasklima/quid", build_vignettes = TRUE) devtools
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:
= c("condition" = "treatment > control") whichConstraint
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:
= c("condition" = "treatment > low_dose", "condition" = "low_dose > control") whichConstraint
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)
<- constraintBF(formula = rtS ~ ID*cond,
resStroop 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:
<- resStroop@generalTestObj
bfs 4] / bfs[3]
bfs[#> 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:
/ max(bfs)
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)
<- constraintBF(formula = rt ~ sub * distance + side,
resLD5 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)