# Specify and fit lba models. Specification of lba models with explanatory variables on the parameters. Models are fitted using full information maximum likelihood. ```r lba(rt, response, data, weights, sddr = ~1, sp = ~1, bound = ~1, nond = ~1, drift = ~1, scaling = "sum", loglink = c(FALSE, FALSE, FALSE, FALSE), sdstart=0.1, startpars, fixed = NULL, method = "L-BFGS-B", hessian = FALSE, lower = -Inf, upper = Inf, fit=TRUE, debug=FALSE) ## S3 method for class 'lba' logLik(object, ...) ## S3 method for class 'lba' print(x, ...) ## S3 method for class 'lba' summary(object, ...) tablba(object) ``` ## Arguments - `rt`: The name of the response time variable in data.frame 'data'. - `response`: The name of the response time variable in data.frame 'data'. - `data`: Data.frame containing the variables. - `weights`: Optional case weights. - `sddr`: The model for the standard deviation of the drift rate, see Details. - `sp`: The model for the start point parameter, see Details. - `bound`: The model for the boundary parameter, see Details. - `nond`: The model for the non-decision time, see Details. - `drift`: The model for the drift rate parameter, see Details. - `scaling`: Options for making the model identifiable; options are "sum" or "fixedSD". - `loglink`: Wheter parameters (sddr, sp, nond, and bound) should be fitted using a log link function (to avoid boundary estimation issues). - `sdstart`: Starting value of the standard deviation of the drift rates in case argument scaling uses option "fixedSD". - `startpars`: Vector of starting values for the parameters. This is currently a required argument as no automatic starting values are available. - `fixed`: Logical; when startpars is given 'fixed' can be used to specify whether parameters should remain fixed during estimation; sometimes required for more stable estimation. - `method`: Optimization method; passed to optim. - `hessian`: Logical; indicating whether the estimated hessian at the minimum; passed to optim. - `lower, upper`: lower and upper boundaries for the parameters; only applicable with optimization method 'L-BFGS-B' is used. - `fit`: Logical; indicating whehter the model should be fit, ie, its parameters optimized or not. Default is TRUE. - `debug`: Logical, default is FALSE; prints out detailed information on submodels, parameters et cetera during optimization. - `object`: a (fitted) lba model. - `x`: a (fitted) lba model. - `...`: not currently in use. ## Details The 5 sub-models of the LBA model can be specified using a formula. Eg, `nond=~diff`, specifies a model in which the `nond`ecision time is modeled as function of `diff`iculty; `diff` may be a factor or numerical variable. Identification of the model is attained by having the drift rates for alternatives in `response` sum to unity or by having a fixed standard deviation of the drift rates. These options are specified by scaling="sum" or scaling="fixedSD", respectively. In the latter case, the value of the fixed standard deviation is assumed to be the first value of `startpars`. If `hessian` is set to TRUE, `optim` is used to get the Hessian at the maximum likelihood estimates of the parameters. This is used in turn to compute standard errors. The `summary` function pretty prints a table of parameter estimates, standard errors, z- and p-values. The `summary` function also prints the separate sub-model specifications and the parameter estimates. The `print` function prints basic information and a (named) vector of parameter estimates. ## Returns The `lba` function returns a list with the following components: - **pars**: The values of fitted parameters. - **logl**: The optimized log likelihood - **convergence**: Convergence information from `optim` - **hessian**: Only included if `hessian` was set to TRUE - **ses**: Only included if `hessian` was set to TRUE and the hessian is non-singular - **fixed**: Vector of logical's indicating whether parameters were fixed - **model**: List of 5 sub-models of the LBA model, see Details above. - **npar**: The number of parameters of the model - **freepars**: The number of freely estimated parameters of the model - **nobs**: The number of observations, used in computing the BIC - **call**: The (matched) call to the `lba` function Function `tablba` returns a `data.frame` with columns: - **value**: The estimated (or fixed) parameter value - **se**: The standard error of the parameter computed from the Hessian - **z**: The z-ratio of `value` and `se` - **p**: The p-value associated with `z` ## References LBA models as in Brown and Heathcote, Cognitive science, 2008. ## Author(s) Ingmar Visser ## Examples ```r data(bh08) # reduce the data set for faster runtimes bh1 <- bh08[c(1:300,1001:1300,2001:2300),] # remove extreme RTs bh1 <- bh1[bh1$rt>.180&bh1$rt<2,] # starting values based on the quantile parameter # estimates from Brown and Heathcote, 2008: # pars <- c(.25,.3,.1,.2,.9,.75,.6) # fit the model with starting values pars <- c(.25,.3,.1,.2,.9,.75,.6) m1 <- lba(rt=rt,response=acc,drift=~diff-1,data=bh1, startpars=pars) m1 summary(m1) ## Not run: # use random starting values instead set.seed(2) m1 <- lba(rt=rt,response=acc,drift=~diff-1,data=bh08, startpars=pars, hessian=TRUE) summary(m1) # get the parameters pp <- m1$pars # simulate some data from the model for the three conditions set.seed(1) dt1 <- rlba(1000, b=pp[3]+pp[2], A=pp[2], vs=c(pp[5],1-pp[5]), s=pp[1], t0=pp[4], truncdrifts=TRUE) dt2 <- rlba(1000, b=pp[3]+pp[2], A=pp[2], vs=c(pp[6],1-pp[6]), s=pp[1], t0=pp[4], truncdrifts=TRUE) dt3 <- rlba(1000, b=pp[3]+pp[2], A=pp[2], vs=c(pp[7],1-pp[7]), s=pp[1], t0=pp[4], truncdrifts=TRUE) dt <- rbind(dt1,dt2,dt3) dt$diff <- gl(3,1000) dt$resp <- ifelse(dt$resp==2,0,1) # remove extreme RTs dt <- dt[dt$rt>.180&dt$rt<2,] # refit the model with the simualted data m1rf <- lba(rt=rt,response=resp,drift=~diff-1,data=dt,startpars=pp) data(numpp1) set.seed(9) m2 <- lba(rt=rt,response=acc,drift=~diff+block,data=numpp1, startpars=c(0.25,runif(4),0,0), scaling="fixedSD", sdstart=0.25, hessian=TRUE) tablba(m2) ## End(Not run) ```

lba function