1130_Homework Exercise 3
Pei-Yun,Li
2020-12-05
1 Description
A computer game simulating the task of an air traffic controller was used in a study of skill aquisition. The objective was to examine the performance of subjects to safely bring in planes. The task was continuous, and the response variable represented the number of planes brought in to land safely every 10min. Subjects were allowed 10-min breaks following completion of each set of three subsequent trials after the initial trial (i.e., after trial 4 and trial 7) to minimize massed practice effects. The sample here consists of 28 subjects. Scores were recorded from the task continuously for a period of 100 minutes, yielding 10 scores. however, scores from the first trial were excluded, allowing for an adjustment period to the task.
Source: Kanfer, R., & Ackerman, P. L. (1989). Motivation and cognitive abilities: An integrative/aptitude-treatment interaction approach to skill acquisition. Journal of Applied Psychology, 74, 657-690.
Column 1: Subject ID
Column 2: Trial number
Column 3: Number of planes
3 Input Data
## 'data.frame': 252 obs. of 3 variables:
## $ ID : chr "S11" "S11" "S11" "S11" ...
## $ Trial: int 1 2 3 4 5 6 7 8 9 1 ...
## $ Plane: int 39 40 47 51 52 50 60 52 56 38 ...4 Lattice Plot
ggplot(dta3, aes(Trial, Plane, group = ID)) +
geom_line() +
geom_point() +
# facet_wrap( ~ ID) +
labs(x = "Trial", y = "Plane")
圖表顯示，多數試驗者試驗次數愈多，其安全降落飛機之次數也愈多。
4.1 By ID
ggplot(dta3, aes(Trial, Plane)) +
geom_line() +
geom_point() +
facet_wrap( ~ ID) +
labs(x = "Trial", y = "Plane")
依據受試者ID重新排序
圖表顯示，試驗者試驗次數增加，其完成任務(安全降落飛機)次數也隨之增加。
推測:是否是因為有練習效果導致?
4.2 By slope
dta3_g <- groupedData(Plane ~ Trial | ID, data = as.data.frame(dta3),
labels = list(x = "Trial", y = "number of planes land safely"),
units = list(x = "(order)", y = "(unit)") )
plot(dta3_g, pch = 1, aspect = .9)
依據斜率重新排序
dta3_init <- c(a = 1, b = log(10/1))
summary(m0 <- nls(Plane ~ a*exp(b*sqrt(Trial)), data = dta3,
start = dta3_init))##
## Formula: Plane ~ a * exp(b * sqrt(Trial))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## a 16.35533 1.17486 13.92 <2e-16 ***
## b 0.30581 0.02953 10.36 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.637 on 250 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 4.348e-075 NLS
ggplot(dta3, aes(Trial, Plane)) +
stat_smooth(method = "nls", formula = y ~ a*exp(b*sqrt(x)),
method.args = list(start = dta3_init),
se = F,
size = rel(.5)) +
geom_point(pch = 1, size = rel(2)) +
scale_x_continuous(limits = c(0, 10), breaks = seq(0, 10, by = 5)) +
scale_y_continuous(limits = c(0, 70), breaks = seq(0, 70, by = 20)) +
facet_wrap( ~ ID) +
labs(x = "Trial (order)",
y = "Number of planes land safely (unit)")
6 NLME
## Warning: 2 times caught the same error in nls(y ~ x/(K + x), data = xy,
## start = list(K = abs(pars[2L]/pars[1L])), algorithm = "plinear"): step factor
## 0.000488281 reduced below 'minFactor' of 0.000976562## Call:
## Model: Plane ~ SSmicmen(Trial, Vm, K) | ID
## Data: dta3_g
##
## Coefficients:
## Vm K
## S37 NA NA
## S32 38.42522 2.6382919
## S21 35.58824 0.6117632
## S26 33.49397 0.8342775
## S31 38.25314 1.4534320
## S29 46.66226 2.9971659
## S35 NA NA
## S23 35.37661 0.6846419
## S27 39.04922 0.8537614
## S28 46.16958 2.2907550
## S33 58.51689 4.8733793
## S34 58.73462 5.3899245
## S36 72.57835 7.9155112
## S14 30.51662 -0.1808489
## S30 48.34655 1.5879277
## S19 41.70994 0.9235549
## S25 46.88423 1.9489698
## S20 45.17192 1.2972892
## S38 102.88531 12.2902544
## S18 45.74841 0.8423952
## S22 45.58569 0.9419266
## S13 43.09619 0.1979081
## S24 70.15462 5.2446174
## S15 46.70072 0.4936488
## S17 52.95904 1.5766528
## S12 53.66601 0.7619322
## S16 54.07300 0.7409107
## S11 58.77729 0.6510748
##
## Degrees of freedom: 234 total; 182 residual
## Residual standard error: 3.575345## Nonlinear mixed-effects model fit by maximum likelihood
## Model: Plane ~ SSmicmen(Trial, Vm, K)
## Data: dta3_g
## AIC BIC logLik
## 1554.784 1575.96 -771.3919
##
## Random effects:
## Formula: list(Vm ~ 1, K ~ 1)
## Level: ID
## Structure: General positive-definite, Log-Cholesky parametrization
## StdDev Corr
## Vm 7.582077 Vm
## K 1.681533 0.441
## Residual 3.861442
##
## Fixed effects: list(Vm ~ 1, K ~ 1)
## Value Std.Error DF t-value p-value
## Vm 45.83635 1.7120608 223 26.772621 0
## K 1.93060 0.3545793 223 5.444764 0
## Correlation:
## Vm
## K 0.546
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.72172107 -0.66635039 -0.03338046 0.57852813 2.08310019
##
## Number of Observations: 252
## Number of Groups: 28## Nonlinear mixed-effects model fit by maximum likelihood
## Model: Plane ~ SSmicmen(Trial, Vm, K)
## Data: dta3_g
## AIC BIC logLik
## 1632.314 1646.431 -812.1568
##
## Random effects:
## Formula: Vm ~ 1 | ID
## Vm Residual
## StdDev: 8.988347 5.192305
##
## Fixed effects: list(Vm ~ 1, K ~ 1)
## Value Std.Error DF t-value p-value
## Vm 42.64821 1.9577317 223 21.78450 0
## K 1.22035 0.1196625 223 10.19829 0
## Correlation:
## Vm
## K 0.439
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.79153678 -0.52887678 -0.03144453 0.53400462 3.16157119
##
## Number of Observations: 252
## Number of Groups: 28
dta3_m1a <- data.frame(dta3, fit = fitted(m1a_g), fit1 = fitted(m1_g))
ggplot(dta3_m1a, aes(Trial, fit)) +
geom_point(aes(Trial, Plane), pch = 1)+
geom_line(col ="steelblue", lwd = .6)+
geom_line(aes(Trial, fit1), col = "indianred", lwd = .6) +
facet_wrap( ~ ID) +
labs(x = "Trial (order)", y = "Number of planes land safely (unit)")