Log-Likelihood functions for the dynWEV and 2DSD models of confidence

Computes the Log-likelihood for given data and parameters in the dynWEV model (Hellmann et al., 2023) and the 2DSD model (Pleskac & Busemeyer, 2010). It is a wrapped version of the respective densities dWEV and d2DSD, where one can find more information about the parameters (z is always given relatively, in the likelihood). The function is mainly used in fitRTConf but exported for individual usage in other contexts.

Usage

LogLikWEV(data, paramDf, model = "dynaViTE", simult_conf = FALSE,
  precision = 1e-05, stop_on_error = TRUE, data_names = list(), ...)

Arguments

data

a dataframe where each row is one trial. Containing following variables:

condition (not necessary; convertible to integer (e.g. factor); for different levels of stimulus quality),
rating (convertible to integer (e.g. factor); discrete confidence judgments),
rt (numeric; giving reaction times for decision task),
stimulus (values at least convertible to c(-1,1); stimulus category (direction of evidence accumulation))
response (characters in "upper", "lower" (or convertible to); direction of decision; correct answers are "lower" for stimulus=-1; and "upper" for stimulus=1),

paramDf

list or data.frame with one row. Names should match the names of dynaViTE and 2DSD model specific parameter names. For different stimulus quality/mean drift rates, names should be v1, v2, v3,.... Different sv and/or s parameters are possible with sv1, sv2, sv3... (s1, s2, s3,... respectively) with equally many steps as for drift rates. Additionally, the confidence thresholds should be given by names with thetaUpper1, thetaUpper2,..., thetaLower1,... or, for symmetric thresholds only by theta1, theta2,... (see Details for the correspondence to the data)

model

character scalar. One of "dynWEV" or "2DSD" for the model to fit.

simult_conf

logical. Whether in the experiment confidence was reported simultaneously with the decision, as then decision and confidence judgment are assumed to have happened subsequent before response and computations are different, when there is an observable interjudgment time (then simult_conf should be FALSE).

precision

numerical scalar. Precision of calculation for integration over z and t0.

stop_on_error

logical. If TRUE an error in the function will be returned in case of invalid parameters. Otherwise, the output will be 0 without error.

data_names

list. Possibility of giving alternative column names for the variables in the data. By default column names are identical to the ones given in the data argument description.

...

Possibility of giving alternative variable names in data frame (in the form condition = "SOA").

Value

Numeric scalar. The summed Log-likelihood of the data given the parameters in the respective model. If one or more row-wise probabilities is <=0, the function returns -1e+12.

Details

Note, that the requirements on the format of the columns for the likelihood functions are much stricter, than in fitRTConf. This is because the function is very frequently calls in the optimization routines of the fitting process and the preprocessing steps are therefore included in that function.

rating, condition. If integer, values should range from 1 to number of possible ratings/conditions. If a factor, the number of levels should be equal to number of possible ratings/conditions. This should be consistent with the parameter vector. The confidence thresholds should be named as thetaUpper1, thetaLower1,.... (or theta1,... for symmetric thresholds), with the number of ratings -1 and the mean drift rates (and possibly the standard deviation in drift rates) should be denoted as v1, v2,... (and sv1, sv2,.../s1, s2, ...) with the number equal to the number of conditions. If only one condition is used v will be accepted as well as v1.

stimulus, response. stimulus should always be given in numerical format with values -1 and 1. response should always be given as a character vector with "lower" and "upper" as values. This corresponds to the situation of Ratcliff's diffusion model (Ratcliff, 1978), where stimulus is the sign of the mean drift direction and the response is the "upper" or "lower" boundary that is first hit by the evidence accumulation. A correct decision is therefore "lower", if stimulus is -1, and "upper", if stimulus is 1.

References

Hellmann, S., Zehetleitner, M., & Rausch, M. (2023). Simultaneous modeling of choice, confidence and response time in visual perception. Psychological Review 2023 Mar 13. doi: 10.1037/rev0000411. Epub ahead of print. PMID: 36913292.

Author

Sebastian Hellmann.

Examples

# 1. Generate data from an artificial participants
# Get random drift direction (i.e. stimulus category) and
# stimulus discriminability (two steps: hard, easy)
stimulus <- sample(c(-1, 1), 200, replace=TRUE)
discriminability <- sample(c(1, 2), 200, replace=TRUE)
# generate data for participant 1
data <- rWEV(200, a=2,v=stimulus*discriminability*0.5,
             t0=0.2,z=0.5, sz=0.1,sv=0.1, st0=0,  tau=4, s=1, w=0.3)
# discretize confidence ratings (only 2 steps: unsure vs. sure)
data$rating <- as.numeric(cut(data$conf, breaks = c(-Inf, 1, Inf), include.lowest = TRUE))
data$participant = 1
data$stimulus <- stimulus
data$discriminability <- discriminability
data <- data[data$response!=0, ] # drop not finished decision processes
data <- data[,-3] # drop conf measure (unobservable variable)
head(data)
#>     rt response rating participant stimulus discriminability
#> 1 0.98       -1      2           1       -1                2
#> 2 1.26       -1      1           1        1                1
#> 3 1.77        1      2           1        1                2
#> 4 1.06        1      2           1        1                1
#> 5 2.05       -1      2           1        1                2
#> 6 0.63       -1      2           1       -1                2

# 2. Define some parameter set in a data.frame
paramDf <- data.frame(a=2.5,v1=0.5, v2=1, t0=0.1,z=0.7,
                      sz=0,sv=0.2, st0=0,  tau=3, w=0.3,
                      theta1=0.8, svis=0.5, sigvis=0.8)

# 3. Compute log likelihood for parameter and data
LogLikWEV(data, paramDf, model="dynWEV", condition="discriminability")
#> [1] -401.5801
# adding the hypothetical interjudgment time to response times
# results in the same log likelihood as before when simult_conf=TRUE
data$rt <- data$rt + paramDf$tau
LogLikWEV(data, paramDf, model="dynWEV", condition="discriminability", simult_conf=TRUE)
#> [1] -401.5801

# the same function for "2DSD" model
paramDf <- data.frame(a=2.5,v1=0.5, v2=1, t0=0.1,z=0.7,
                      sz=0,sv=0.2, st0=0,  tau=3, theta1=0.8)
LogLikWEV(data, paramDf, model="2DSD", condition="discriminability", simult_conf=TRUE)
#> [1] -429.6288
# this results in the same log likelihood as before