Description Usage Arguments Details Value Note Author(s) References See Also Examples

Parameter estimation for reaction time distributions using the maximum likelihood method. Currently, the function works only for the ex-Gaussian probability distribution.

1 2 |

`x` |
Vector of reaction times, in milliseconds or seconds. |

`iter` |
if |

`size` |
Sample dimension to use in resampling, when the bootstrap is active. |

`replace` |
Logical: specifies if the resampling must be performed with replacement. |

`plot` |
Logical: if |

`start` |
Vector containing starting values (in order: |

`...` |
Further arguments for the optimization routine. Arguments will be passed to the |

The function `timefit`

estimates ex-Gaussian parameters by maximum likelihood, using the
`optim`

function. As default, the Simplex method (Nelder-Mead) is applied to find the
minimum of the objective function.

The function implements a bootstrap approach to identify distribution parameters. The bootstrap
is useful especially working on small samples. The implemented method identifies *μ* and
*σ* using a gaussian kernel estimator (see Van Zandt, 2000, for details). Since small
samples often present problems of convergence for *σ*, for this parameter only the
values included a theoretical plausible range are considered. This range is defined by:

* √{\frac{min(x-M)^2}{n-1}} ≤q σ ≤q S *

where M and S are respectively the mean and the standard deviation of data. When *μ* and
*σ* are identified, *τ* is chosen within the bootstrapped values, according to
the maximum likelihood criterion.

An object of class `timefit`

. The operator `@`

should be used to extract the values
from the slots of the output object.

@x: vector of data.

@samples: bootstrapped samples.

@par: estimated parameters.

@bootPar: bootstrapped parameters.

@bootValue: log-likelihood of bootstrapped parameters.

@sigmaValid: not rejected (

`TRUE`

) and rejected (`FALSE`

) values for*σ*.@start: starting values.

@logLik: log-likelihood of estimated parameters.

@AIC: Akaike Information Criterion.

@BIC: Bayesian Information Criterion.

The methods `plot`

, `logLik`

, `AIC`

and `BIC`

are available.

Davide Massidda [email protected]

Cousineau, D., Brown, S. & Heathcote, A. (2004). Fitting distributions using maximum likelihood: Methods and packages. Behavior Research Methods, Instruments, & Computers, 36(4), 742-756.

Heathcote, A. (1996). RTSYS: A DOS application for the analysis of reaction time data. Behavior Research Methods, Instruments, & Computers, 28(3), 427<e2><80><93>445.

Lacouture, Y., & Cousineau, D. (2008). How to use MATLAB to fit the ex-Gaussian and other probability functions to a distribution of response times. Tutorials in Quantitative Methods for Psychology, 4(1), 35-45.

Luce, R. D. (1986). Response times: their role in inferring elementary mental organization. New York: Oxford University Press.

Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85(2), 59-108.

Ratcliff, R. (1979). Group Reaction Time Distributions and an Analysis of Distribution Statistics. Psychological Bulletin, 86(3), 446-461.

Ratcliff, R. & Murdock Jr., B. B. (1976). Retrieval Processes in Recognition Memory. Psychological Review, 83(3), 190-214.

Van Zandt, T. (2000). How to fit a response time distribution. Psychonomic Bulletin & Review, 7(3), 424-465.

Van Zandt, T.(2002). Analysis of response time distributions. In J. T. Wixted (Vol. Ed.) & H. Pashler (Series Ed.): Stevens' Handbook of Experimental Psychology (3rd Edition), Volume 4: Methodology in Experimental Psychology (pp. 461-516). New York: Wiley Press.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
## Not run:
# Vector of reaction times from Heathcote (1996):
RT <- c(474.688, 506.445, 524.081, 530.672, 530.869,
566.984, 582.311, 582.940, 603.574, 792.358)
RTfit <- timefit(RT); RTfit
# Boostrap tesing with simulated data (m=500, s=100, t=250):
x1 <- c(451.536,958.612,563.538,505.735,1266.825,
860.663,457.707,268.679,587.303,669.594)
fit1a <- timefit(x1); fit1a
fit1b <- timefit(x1, iter=1000); fit1b
x2 <- c(532.474,525.185,1499.471,480.732,631.752,
672.419,322.341,571.356,428.832,680.848)
fit2a <- timefit(x2, plot=TRUE); fit2a
fit2b <- timefit(x2, iter=1000, plot=TRUE); fit2b
## End(Not run)
``` |

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