# Log-Likelihood functions for the independent and partially anti-correlated race models of confidence Computes the Log-likelihood for given data and parameters in the IRM and PCRM with or without time-scaled confidence measure. It is a wrapped version of the respective densities `dIRM` and `dPCRM`, where one can find more information about the parameters. It restricts the rates of accumulation to be the negative of each other, though (a common assumption in perceptual decision tasks). The function is mainly used inside `fitRTConf` for race models but exported for individual usage in other contexts. ```r LogLikRM(data, paramDf, model = "IRM", time_scaled = FALSE, precision = 6, 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(1,2), i.e. integer or factor; stimulus category (index of accumulator with higher drift)) * response (values at least convertible to c(1,2); direction of decision; (index of accumulator reaching the boundary first)) - `paramDf`: a list or data frame with one row. Column names should match the names of RaceModels parameter names (only `mu1` and `mu2` are not used in this context but replaced by the parameter `v`). For different stimulus quality/mean drift rates, names should be `v1`, `v2`, `v3`,.... Different `s` parameters are possible with `s1`, `s2`, `s3`,... 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 "IRM" or "PCRM". ("IRMt" and "PCRMt" will also be accepted. In that case, time_scaled is set to TRUE.) - `time_scaled`: logical. Whether the confidence measure should be scaled by 1/sqrt(rt). Default: TRUE. - `precision`: numerical scalar. Precision of calculation for integration over t0. - `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. - `...`: Another possibility of giving alternative variable names in data frame (in the form `condition = "SOA"`). ## Returns 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 called in the optimization routines of the fitting process and the preprocessing steps are therefore included in the other function. rating, condition . If integer, values should range from 1 to number of possible ratings/conditions. If 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 `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 and response should always be given in numerical format with values 1 and 2. Stimulus determines which of two accumulators has positive drift. The other has negative drift with the same absolute value. Response gives the index of the accumulator that reaches the boundary first. ## Examples ```r # 1. Generate data from an artificial participants # Get random index for accumulator with positive # drift (i.e. stimulus category) and # stimulus discriminability (two steps: hard, easy) stimulus <- sample(c(1, 2), 200, replace=TRUE) discriminability <- sample(c(1, 2), 200, replace=TRUE) # generate data for participant 1 data <- rPCRM(200, mu1=ifelse(stimulus==1, 1, -1)*discriminability*0.5, mu2=ifelse(stimulus==1, -1, 1)*discriminability*0.5, a=2, b=1.8, t0=0.2, st0=0, wx=0.7, wint=0.3, wrt=0) # discretize confidence ratings (only 2 steps: unsure vs. sure) data$rating <- as.numeric(cut(data$conf, breaks = c(0, 3, Inf), include.lowest = TRUE)) data$stimulus <- stimulus data$discriminability <- discriminability data <- data[data$response!=0, ] # drop not finished decision processes data <- data[,-c(3,4)] # drop xl and conf measure (unobservable variable) head(data) # 2. Define some parameter set in a data.frame paramDf <- data.frame(a=2,b=2, v1=0.5, v2=1, t0=0.1,st0=0, wx=0.6, wint=0.2, wrt=0.2, theta1=4) # 3. Compute log likelihood for parameter and data LogLikRM(data, paramDf, model="PCRMt", condition="discriminability") # same result LogLikRM(data, paramDf, model="PCRM", time_scaled=TRUE,condition="discriminability") # different LogLikRM(data, paramDf, model="PCRM", condition="discriminability") # same parameters used for IRM model LogLikRM(data, paramDf, model="IRMt", condition="discriminability") ``` ## Author(s) Sebastian Hellmann.

LogLikRM function