Each accumulation task trial begins with the onset of the center LED, which signals to the rat to enter the center port. The subject holds his nose in the center port for 2 s, until the center LED …
(A) Behavior as a function of total right minus total left clicks. For very easy trials (large click differences) performance is ≈90% correct. The circles (with very small error bars) are the mean …
At each timepoint, the accumulator memory a (black trace) represents an estimate of the ‘Right’ vs ‘Left’ evidence accrued so far. At stimulus end, the model decides ‘Right’ if a > Þ, the decision …
(A) Behavior as a function of total right minus total left clicks. For very easy trials (large click differences) performance is ≈90% correct. The thick line is the average performance of the 14 …
(A) Top-down view of rat cortex with the locations of the FOF and the PPC, into which cannulae were implanted. (B) Bilateral infusion of muscimol into the FOF results in a substantial impairment on …
(A–C) The targets of cannula implants for group 1,2, and 3 with the list of the rats in each group. (D) A birds-eye view of rat T061's brain after fixation and removal from the skull. The AP and ML …
Each point of the figure is the bias for a single session (%Right − %Left Correct). The number at the beginning of the x-axis indicates the days passed since surgical implantation with cannula. …
The psychometric data and GLMM model fits for bilateral FOF infusions in each rat (n = 4). Open circles are binned data from accumulation trials and the small points are the predictions of the GLMM …
(A) When analyzed in terms of the psychometric function, changes to either lapse rate alone or accumulation time constant alone can match the bilateral FOF inactivation data. The black line shows …
MATLAB file containing resampled bilateral FOF model fits.
This MATLAB file contains three variables. BF: a 300 × 9 matrix. Each row is the set of parameters which maximized the likelihood of the accumulator model fit to a resampling of the bilateral FOF data. Each column is a parameter. LL: a 300 × 1 vector with the negative log likelihood of the corresponding row of BF. parameter_names: a 9 × 1 cell with the names of the columns of BF.
(A) Post-categorization bias: after categorizing the accumulator value into ‘Go Left’ or ‘Go Right’ decisions, a fraction, κL, of Left decisions are reversed into Right decisions, and a fraction, κR,…
(A) A comparison of the likelihoods (i.e., best model fits) for the four different bias mechanisms illustrated in Figure 5. The post-categorization bias model is better than the next best model …
Top row: For all curves, the circles with error bars indicate fraction of Contra choice trials (mean ± se) across trial groups, with different groups having different #Contra − #Ipsi clicks. The …
Using the Metropolis–Hastings algorithm we collected 40,000 samples from an 8-parameter model of the unilateral FOF inactivation. The parameters are the rows and columns of this matrix of plots. The …
(A) As in Figure 3B, but for unilateral infusions of muscimol into the PPC, which result in a minimal impairment. In black are data from control sessions 1 day before an infusion (n = 65 sessions, …
(A) The psychometric data for accumulation trials and GLMM model fits for bilateral PPC infusions in each rat (n = 4). Open circles are binned data and the small points are the predictions of the …
Infusions into the FOF are in magenta and into the PPC are in yellow. Circles indicate bias on LED trials, squares indicate bias on accumulation trials. The magenta line is the linear fit between …
(A–D) Effect of unilateral PPC or FOF inactivations on free choice trials intermixed with regular accumulation trials. (A) A schematic of the three interleaved trial types: Accumulation, Side LED …
The psychometric data for accumulation trials and GLMM model fits for bilateral FOF infusions in each rat (n = 4). Open circles are binned data and the small points are the predictions of the GLMM …
Best-fit parameters
Ratname | λ | B | ϕ | τϕ | Þ | lapse | |||
---|---|---|---|---|---|---|---|---|---|
B115 | 1.409 | 0.113 | 102.130 | 0.523 | 14.849 | 0.175 | 0.064 | 0.157 | 0.094 |
T055 | 1.226 | 0.001 | 11.248 | 0.043 | 16.014 | 0.253 | 0.351 | 0.118 | 0.078 |
T057 | 0.810 | 0.031 | 74.478 | 0.027 | 15.060 | 0.156 | 0.093 | 0.020 | 0.075 |
T058 | 1.087 | 0.000 | 17.612 | 0.000 | 15.875 | 0.025 | 0.276 | −0.122 | 0.051 |
T061 | 0.620 | 0.000 | 96.545 | 0.502 | 16.038 | 0.380 | 0.041 | 0.236 | 0.066 |
T062 | −0.098 | 0.000 | 49.361 | 0.619 | 15.761 | 0.139 | 0.047 | 0.518 | 0.083 |
A065 | 2.047 | 0.000 | 37.685 | 0.207 | 15.729 | 0.147 | 0.092 | −0.465 | 0.031 |
A066 | 0.349 | 0.000 | 15.565 | 0.000 | 12.705 | 0.072 | 0.462 | 0.041 | 0.170 |
A077 | −2.739 | 0.197 | 128.586 | 22.801 | 9.253 | 0.184 | 0.031 | 0.886 | 0.001 |
A078 | −2.070 | 0.000 | 104.688 | 0.000 | 18.086 | 0.283 | 0.026 | 0.062 | 0.063 |
A060 | −1.542 | 0.000 | 54.786 | 0.000 | 15.416 | 0.010 | 0.115 | 0.180 | 0.245 |
A062 | 2.258 | 0.296 | 156.860 | 0.486 | 16.839 | 0.527 | 0.076 | 0.466 | 0.119 |
A083 | −0.790 | 47.441 | 31.788 | 1.384 | 16.282 | 0.015 | 0.059 | 0.033 | 0.107 |
A084 | 1.371 | 0.064 | 70.267 | 1.690 | 15.011 | 0.016 | 0.086 | 0.467 | 0.110 |
Meta-Rat | 1.227 | 0.001 | 57.614 | 0.043 | 16.042 | 0.221 | 0.109 | 0.065 | 0.102 |
BiFOF | −4.144* | 62.423 | 237.642 | 1.754 | 22.013 | 0.082 | 0.039 | 0.737* | 0.010 |
BiPPC | 1.331 | 0.531 | 42.175 | 0.000 | 14.860 | 0.512 | 0.175 | −0.249 | 0.321 |
This table shows the values of the parameters which maximize the likelihood of the full 9-parameter accumulator model for each rat, as well as for the ‘meta-rat’ (made from taking all of the control days that were 1 day before an infusion, n = 47,580 trials), the fit to the bilateral FOF data (n = 1809), and the fit to the bilateral PPC data (n = 1569).
indicate parameters that were significantly different from the control ‘Meta-Rat’.
Bilateral FOF model comparison
Model | # of param. | Log likelihood | BIC | AIC |
---|---|---|---|---|
full model | 9 | −1102.5 | 2272.5 | 2223† |
Þ model | 1 | −1221.6 | 2450.7 | 2445.2 |
λ model | 1 | −1121.1 | 2249.7* | 2244.2 |
This table shows the three models fit to the bilateral FOF data (n = 1809 trials).
indicates the model with the lowest (the most likely) Bayesian information criterion (BIC).
indicates the model with the lowest (most informative) Akaike information criterion (AIC).
In this case, the AIC and BIC select different models, suggesting a better model may be somewhere in between. That is, a model that includes the accumulator time-constant and perhaps a few additional parameters from the full model.
Unilateral FOF model comparison
Model | # of parameters | Log likelihood | BIC | AIC |
---|---|---|---|---|
Post-categorization bias | 1 | −1963.1 | 3934.4* | 3928.2† |
Unbalanced input gain | 1 | −2013.1 | 4034.4 | 4028.2 |
Accumulator shift | 1 | −2217.4 | 4443.0 | 4436.8 |
Unbalanced input noise | 1 | −2272.7 | 4553.7 | 4547.4 |
8-parameter model | 8 | −1957.5 | 3981.1 | 3949.9 |
This table shows the three models fit to the unilateral FOF data (n = 3836 trials).
indicates the model with the lowest Bayesian information criteria (BIC), that is, the most likely model.
indicates the model with the lowest Akaike information criteria (AIC), that is, the most informative model.
The 1-parameter post-categorization model has the lowest AIC and BIC, supporting the view that the major effect of unilateral FOF inactivation is not related to the accumulation process per se.
Using the lme4 package to fit generalized-liner mixed models in R. This file contains the code (and links to our data) which shows how we used the lme4 package, in R, to fit generalized linear mixed models (GLMM). We also include the output of each of the GLMM we described in the main text. This allows the interested reader to regenerate our main results and also, by providing the data, allows the reader to perform additional statistical tests.