I am looking for an implementation of the linear ballistic accumulator model or Ratcliff's diffusion model (e.g. in R, MATLAB, or Python).
Here are a few options. I have not tried them yet personally.
Scott Brown has a copy of Donkin et al (2009) on his web page with some code in R, Excel, and WinBUGS for fitting the LBA model:
There's also the
The Diffussion model is available as a matlab toolbox called (DMAT).
For the diffusion model, there is also Eric-Jan Wagenmakers' "EZ-diffusion model", which you can find here.
This paper compares three different pieces of software for estimation of diffusion model parameters:
The R package diffIRT (http://www.dylanmolenaar.nl/jss1265.pdf) estimates both the Q and the D diffusion models (see his website for the van der Maas et al. paper discussing the differences between these models). R code for the EZ2 approach, which is much faster if that is important for your applications, is http://raoul.socsci.uva.nl/EZ2/.