Description Usage Arguments Details Value Author(s) References See Also Examples
Calculates the Capacity Coefficient for First-Terminating (OR) Processing
1 | capacity.or(RT, CR=NULL, ratio=TRUE)
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RT |
A list of response time arrays. The first array in the list is assumed to be the exhaustive condition. |
CR |
A list of correct/incorrect indicator arrays. If NULL, assumes all are correct. |
ratio |
Indicates whether to return the standard ratio capacity coefficient or, if FALSE, the difference form. |
The OR capacity coefficient compares performance on task to an unlimited-capacity, independent, parallel (UCIP) model using cumulative hazard functions. Suppose Hi(t) is the cumulative hazard function for response times when process i is completed in isolation and Hi(t) is the cumulative hazard function for response times when all processes occur together and a response is made as soon as any of the processes finish. Then the OR capacity coefficient is given by,
Cor(t)=sum[Hor(t)]/[Hi(t)].
The denominator is the estimated cumulative hazard function for the UCIP model, based on the response times for each process in isolation and the numerator is the actual performance.
Cor(t)<1 implies worse performance than the UCIP model. This indicates that either there are limited processing resources, there is inhibition among the subprocesses, or the items are not processed in parallel (e.g., the items may be processed serially).
Cor(t)>1 implies better performance than the UCIP model. This indicates that either there are more processing resources available per process when there are more processes, that there is facilitation among the subprocesses, or the items are not processed in parallel (e.g., the items may be processed coactively).
The difference form of the capacity coefficient is given by,
Cor(t)=Hor(t) - sum[Hi(t)].
Negative values indicate worse than UCIP performance and positive values indicate better than UCIP performance.
Ct |
An object of class approxfun representing the OR capacity coefficient. |
Var |
An object of class approxfun representing the variance of the estimated AND capacity coefficient. Only returned if ratio=FALSE. |
Ctest |
A list with class "htest" that is returned from |
Joe Houpt <joseph.houpt@wright.edu>
Townsend, J.T. & Nozawa, G. (1995). Spatio-temporal properties of elementary perception: An investigation of parallel, serial and coactive theories. Journal of Mathematical Psychology, 39, 321-360.
Houpt, J.W. & Townsend, J.T. (2012). Statistical Measures for Workload Capacity Analysis. Journal of Mathematical Psychology, 56, 341-355.
Houpt, J.W., Blaha, L.M., McIntire, J.P., Havig, P.R. and Townsend, J.T. (2013). Systems Factorial Technology with R. Behavior Research Methods.
ucip.test
capacityGroup
capacity.and
estimateUCIPor
estimateNAH
approxfun
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | rate1 <- .35
rate2 <- .3
RT.pa <- rexp(100, rate1)
RT.ap <- rexp(100, rate2)
RT.pp.limited <- pmin( rexp(100, .5*rate1), rexp(100, .5*rate2))
RT.pp.unlimited <- pmin( rexp(100, rate1), rexp(100, rate2))
RT.pp.super <- pmin( rexp(100, 2*rate1), rexp(100, 2*rate2))
tvec <- sort(unique(c(RT.pa, RT.ap, RT.pp.limited, RT.pp.unlimited, RT.pp.super)))
cap.limited <- capacity.or(RT=list(RT.pp.limited, RT.pa, RT.ap))
print(cap.limited$Ctest)
cap.unlimited <- capacity.or(RT=list(RT.pp.unlimited, RT.pa, RT.ap))
cap.super <- capacity.or(list(RT=RT.pp.super, RT.pa, RT.ap))
matplot(tvec, cbind(cap.limited$Ct(tvec), cap.unlimited$Ct(tvec), cap.super$Ct(tvec)),
type='l', lty=1, ylim=c(0,3), col=2:4, main="Example Capacity Functions", xlab="Time",
ylab="C(t)")
abline(1,0)
legend('topright', c("Limited", "Unlimited", "Super"), lty=1, col=2:4)
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Loading required package: fda
Loading required package: splines
Loading required package: Matrix
Attaching package: 'fda'
The following object is masked from 'package:graphics':
matplot
Houpt-Townsend UCIP test
data: RT and CR
z = -5.151, p-value = 2.591e-07
alternative hypothesis: response times are different than those predicted by the UCIP-OR model
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