EllipseData: Simulated Ellipse Data for 6 Ellipses with period=24.

In hysteresis: Tools for Modeling Rate-Dependent Hysteretic Processes and Ellipses

Description

Three subjects with two replications = 6 ellipses created by mel. All 6 ellipses are centered around the origin with a phase angle of pi/2 and differ by subject in terms of their retention (0.4,0.8,0.4) and b.x saturation point (0.6,0.6,1). Errors in both the input and the output are given a standard deviation of 0.1 for all ellipses. Used in the help page for fel.repeated.

Usage

data(EllipseData)

Format

A data frame with 144 observations on the following 4 variables.

X

a numeric vector

Y

a numeric vector

subjects

subject, one of "A", "B", or "C".

repeated

which ellipse for subject. Either 1 or 2.

Examples

## Data is created using the following code
set.seed(1)
ellip1 <- mel(method = 2, retention = 0.4, b.x = 0.6, b.y = 0.8, cx = 0, cy = 0, 
    sd.x = 0.1, sd.y = 0.1, period = 24, n.points = 48, phase.angle = pi/2)
ellip2 <- mel(method = 2, retention = 0.8, b.x = 0.6, b.y = 0.8, cx = 0, cy = 0, 
    sd.x = 0.1, sd.y = 0.1, period = 24, n.points = 48, phase.angle = pi/2)
ellip3 <- mel(method = 2, retention = 0.4, b.x = 1, b.y = 0.8, cx = 0, cy = 0, 
    sd.x = 0.1, sd.y = 0.1, period = 24, n.points = 48, phase.angle = pi/2)
X <- c(ellip1$x, ellip2$x, ellip3$x)
Y <- c(ellip1$y, ellip2$y, ellip3$y)
subjects <- c(rep("A", length(ellip1$x)), rep("B", length(ellip2$x)), rep("C", 
    length(ellip3$x)))  
    repeated <- rep(c(1,2),each=24,times=3)  
    
##Use data file to fit 6 ellipses.
data(EllipseData) 
six.models <- fel.repeated(EllipseData$X, EllipseData$Y, method = "harmonic2",
subjects = EllipseData$subjects,repeated=EllipseData$repeated)
six.models
 
#Model fit for B-1
six.models$models["B",1] 
par(mfrow=c(2,3))
plot(six.models,xlab="X input",ylab="Y output")
par(mfrow=c(1,1))

Example output

Loading required package: car
Loading required package: carData
Loading required package: msm
Loading required package: MASS
Call:
fel(x = x, y = y, method = "harmonic2", subjects = subjects2, 
    subset = subset)

Parameter Estimates:
  subjects repeated       b.x       b.y phase.angle           cx           cy
1        A        1 0.5736708 0.7912104   -4.695827 -0.020697918 -0.019671309
2        B        1 0.5502696 0.8478535    1.522854  0.018284077 -0.007561673
3        C        1 0.9989673 0.8180595   -4.676999 -0.004129446 -0.015904305
4        A        2 0.5926083 0.8083487   -4.661392 -0.010540786 -0.016880005
5        B        2 0.5961080 0.7700083   -4.668501  0.033268300  0.025867810
6        C        2 0.9935576 0.8126730   -4.711277  0.029901050  0.026175462
  retention  coercion      area      lag split.angle hysteresis.x hysteresis.y
1 0.3762420 0.2463602 0.6780785 1.695490    54.05583    0.4294452    0.4755272
2 0.8171985 0.3818710 1.4127098 2.929684    57.01583    0.6939708    0.9638440
3 0.4144164 0.4514399 1.3005830 1.791072    39.31422    0.4519066    0.5065847
4 0.4272710 0.2769307 0.7954650 1.857314    53.75449    0.4673082    0.5285727
5 0.8502358 0.4418421 1.5922607 3.188982    52.25447    0.7412116    1.1041904
6 0.3679489 0.4098001 1.1484985 1.623953    39.28119    0.4124574    0.4527638
       ampx      ampy rote.deg  rote.rad semi.major semi.minor   focus.x
1 0.5736708 0.8761118 57.89057 1.0103811   1.025867  0.2103967 0.5336960
2 0.5502696 1.1775691 69.63757 1.2154049   1.248931  0.3600515 0.4161244
3 0.9989673 0.9170399 42.25702 0.7375241   1.319251  0.3138056 0.9483996
4 0.5926083 0.9143238 58.42020 1.0196249   1.063230  0.2381463 0.5426518
5 0.5961080 1.1470892 68.14732 1.1893951   1.224701  0.4138415 0.4290453
6 0.9935576 0.8920896 41.62150 0.7264323   1.305594  0.2800093 0.9532846
    focus.y eccentricity
1 0.8504735    0.9787428
2 1.1211743    0.9575438
3 0.8616776    0.9712979
4 0.8827652    0.9745929
5 1.0698359    0.9411776
6 0.8470057    0.9767308

Delta Method Standard Errors:
  subjects repeated     b.x     b.y phase.angle      cx      cy retention
1        A        1 0.03591 0.03035     0.06259 0.02539 0.02146   0.03035
2        B        1 0.02605 0.02935     0.04733 0.01842 0.02075   0.02935
3        C        1 0.02949 0.02961     0.02952 0.02085 0.02093   0.02961
4        A        2 0.02640 0.02487     0.04455 0.01867 0.01759   0.02487
5        B        2 0.02060 0.02373     0.03456 0.01457 0.01678   0.02373
6        C        2 0.02933 0.02873     0.02952 0.02074 0.02032   0.02873
  coercion    area     lag split.angle    ampx    ampy rote.deg
1  0.02366 0.06923 0.13231     0.03489 0.03591 0.03035    3.291
2  0.02060 0.08394 0.09519     0.02678 0.02605 0.02935    1.440
3  0.03171 0.10053 0.12331     0.02289 0.02949 0.02961    2.554
4  0.01885 0.05831 0.10391     0.02582 0.02640 0.02487    2.200
5  0.01737 0.07073 0.07901     0.02241 0.02060 0.02373    1.107
6  0.03156 0.09587 0.12302     0.02257 0.02933 0.02873    2.929
[[1]]
Call:
FUN(x = data[x, , drop = FALSE], method = ..1, period = ..2, 
    times = ..3, na.action = ..4, control = ..5)

Delta Method Standard Errors and 95% C.I.'s:
            Estimates    S.E.      low     high
b.x          0.550270 0.02605  0.49555  0.60499
b.y          0.847854 0.02935  0.78620  0.90951
phase.angle  1.522854 0.04733  1.42341  1.62230
cx           0.018284 0.01842 -0.02041  0.05698
cy          -0.007562 0.02075 -0.05116  0.03603
retention    0.817199 0.02935  0.75554  0.87885
coercion     0.381871 0.02060  0.33860  0.42514
area         1.412710 0.08394  1.23637  1.58905
lag          2.929684 0.09519  2.72970  3.12967
split.angle 57.015828 0.02678 56.95957 57.07209
ampx         0.550270 0.02605  0.49555  0.60499
ampy         1.177569 0.02935  1.11592  1.23922
rote.deg    69.637569 1.43951 66.61326 72.66188

hysteresis documentation built on May 15, 2021, 1:09 a.m.