statConfR: Models of Decision Confidence and Metacognition

The statConfR package provides functions to fit static models of decision-making and confidence derived from signal detection theory for binary discrimination tasks, as well as meta-d′/d′ (Rausch & Hellmann, 2024). The package can be used to test the assumptions underlying meta-d′/d′. Several models provide a metacognition parameter that may serve as an alternative when the assumptions of meta-d′/d′ assuming the corresponding model provides a better fit to the data. At this point in time, the following models are included:

• Signal detection rating model

• Gaussian noise model

• Weighted evidence and visibility model

• Post-decisional Accumulation Model

• Independent Gaussian model

• Independent truncated Gaussian model (the model underlying the meta-d′/d′ method, see Rausch et al., 2023)

• Lognormal noise model

• Lognormal weighted evidence and visibility model

Installation

The latest released version of the package is available on CRAN via

install.packages("statConfR")

The easiest way to install the development version is using devtools and install from GitHub:

devtools::install_github("ManuelRausch/StatConfR")

Usage

Data structure

The package includes a demo data set from a masked orientation discrimination task with confidence judgments (Hellmann et al., 2023, Exp. 1.

library(statConfR)
data("MaskOri")
head(MaskOri)

##   participant stimulus correct rating diffCond trialNo
## 1           1        0       1      0      8.3       1
## 2           1       90       0      4    133.3       2
## 3           1        0       1      0     33.3       3
## 4           1       90       0      0     16.7       4
## 5           1        0       1      3    133.3       5
## 6           1        0       1      0     16.7       6

Data should be in the form of a data.frame object columns for following variables:

• stimulus (factor with 2 levels): The property of the stimulus which defines which response is correct
• diffCond (factor): The experimental manipulation that is expected to affect discrimination sensitivity
• correct (0-1): Indicating whether the choice was correct (1) or incorrect(0).
• rating (factor): A discrete variable encoding the decision confidence (high: very confident; low: less confident)
• participant (integer): giving the subject ID.

Fitting

It is strongly recommended that if metacognitive efficiency is to be measured using the meta-d′/d′ method that researchers fist determine whether the Independent Truncated Gaussian Model, the confidence model implied by the meta-d′/d′ method, is an adequate description of the data. Using the function fitConfModel, we can fit several confidence models to the data of each participant. The argument .parallel=TRUEallows for parallelization over all but one available core.

fitted_pars <- fitConfModels(MaskOri, models=c("SDT", "WEV"), .parallel = TRUE) 

This parallelizes the fitting process over participant-model combinations. The output is then a data frame with one row for each participant-model combination and columns for parameters and measures for model performance (negative log-likelihood, BIC, AIC and AICc). These may be used for quantitative model comparison.

head(fitted_pars)

##   model participant negLogLik    N  k      BIC     AICc      AIC    d_1    d_2
## 1   SDT           1  2721.256 1620 14 5545.975 5470.739 5470.513 0.0428 0.4593
## 2   WEV           1  2621.110 1620 16 5360.464 5274.520 5274.221 0.2027 0.6142
## 3   SDT           2  1946.258 1620 14 3995.979 3920.743 3920.517 0.0000 0.0950
## 4   WEV           2  1827.221 1620 16 3772.684 3686.741 3686.441 0.0512 0.1920
## 5   SDT           3  1706.178 1620 14 3515.818 3440.582 3440.356 0.2708 0.4673
## 6   WEV           3  1661.617 1620 16 3441.476 3355.533 3355.233 0.4146 0.8561
##      d_3    d_4    d_5       c theta_minus.4 theta_minus.3 theta_minus.2
## 1 1.0526 3.6806 4.7779 -0.2723       -1.5467       -1.0333       -0.6336
## 2 1.0797 3.4746 4.0799 -0.2957       -2.0665       -1.2485       -0.4152
## 3 0.8601 6.1410 8.0556 -0.1394       -2.0092       -1.9193       -1.4097
## 4 1.0412 4.1423 5.2886 -0.1475       -2.0441       -1.9500       -1.3982
## 5 1.9117 6.4257 7.5755 -1.1510       -1.9938       -1.6372       -1.2600
## 6 2.7115 6.9164 7.9863 -1.3743       -2.7625       -1.9192       -0.3724
##   theta_minus.1 theta_plus.1 theta_plus.2 theta_plus.3 theta_plus.4  sigma
## 1       -0.4543      -0.0944       0.2152       0.9850       1.5735     NA
## 2        0.1296      -0.6196       0.1544       1.3976       2.1879 1.0105
## 3       -0.9580       0.7857       1.3781       2.0879       2.2369     NA
## 4       -0.9030       0.8201       1.4484       2.2447       2.4030 0.6391
## 5       -1.1668      -1.1143      -0.7344       0.2961       0.9314     NA
## 6        0.9328      -2.7695      -1.1313       0.7714       1.7520 1.3289
##        w wAIC wAICc wBIC
## 1     NA    0     0    0
## 2 0.5361    1     1    1
## 3     NA    0     0    0
## 4 0.5020    1     1    1
## 5     NA    0     0    0
## 6 0.3818    1     1    1

If the Independent Truncated Gaussian model provides a decent account of the data (which is not the case though in the demo dataset), it is legitimate to quantify metacognitive efficiency with meta-d′/d′:

MetaDs <- fitMetaDprime(subset(MaskOri, diffCond == "33.3"), 
                        model="ML", .parallel = TRUE)

Contact

For comments, remarks, and questions please contact either manuel.rausch@hochschule-rhein-waal.de or sebastian.hellmann@ku.de or submit an issue.

References

Hellmann, S., Zehetleitner, M., & Rausch, M. (2023). Simultaneous modeling of choice, confidence, and response time in visual perception. Psychological Review. 130(6), 1521–1543. doi:10.1037/rev0000411

Rausch, M., Hellmann, S. & Zehetleitner, M. (2023). Measures of metacognitive efficiency across cognitive models of decision confidence. Psychological Methods. doi:10.1037/met0000634

Rausch, M., & Hellmann, S. (2024). statConfR: An R Package for Static Models of Decision Confidence and Metacognition. PsyArXiv. doi:10.31234/osf.io/dk6mr