My name is Giovanna and I am a PhD student in Norway.
I am a beginner with statistics and R,  hence my ignorance. Apologies from now.....

I have been collecting data on time performances of 5 subjects using a 1:3 scale tower yarder. The task was consisting in yarding 5 small logs placed on permanently marked course. Four subjects had different previous experiences (None, Some) and the fifth was a trainer (Control).
Each cycle time per each log was registered, the sum of the 5 logs' cycle time was giving the replication time. We had 6 replication per subject .
I would like to predict the time necessary to perform the task.

I have been modelling the time to perform the task (prod.time)versus the replication number (Trial-in the dataset), the previous experience (factor) and their interaction. As random effect I have been using the subjects.



> ma<-lme(prod.time~Trial+Previous.experience+Trial*Previous.experience, data=  Data27_04, random=~1|Student, method="ML")
> summary(ma)
Linear mixed-effects model fit by maximum likelihood
Data: Data27_04
       AIC      BIC    logLik
  1517.445 1541.259 -750.7226

Random effects:
Formula: ~1 | Student
        (Intercept) Residual
StdDev:    7.337648 42.42332

Fixed effects: prod.time ~ Trial + Previous.experience + Trial * Previous.experience
                               Value Std.Error  DF   t-value p-value
(Intercept)                102.44173  9.561987 137 10.713435  0.0000
Trial                       -6.48494  2.252271 137 -2.879291  0.0046
Previous.experience1       -37.36173 14.786033   2 -2.526826  0.1274
Previous.experience2        47.22627 12.451072   2  3.792948  0.0630
Trial:Previous.experience1   6.55351  3.496401 137  1.874360  0.0630
Trial:Previous.experience2  -7.55163  2.940879 137 -2.567813  0.0113
Correlation:
                           (Intr) Trial  Prvs.1 Prvs.2 Tr:P.1
Trial                      -0.841
Previous.experience1        0.253 -0.208
Previous.experience2       -0.234  0.199 -0.540
Trial:Previous.experience1 -0.207  0.264 -0.835  0.447
Trial:Previous.experience2  0.199 -0.226  0.447 -0.836 -0.550

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max
-2.3519731 -0.6903211 -0.1031114  0.6503216  4.6699702

Number of Observations: 145
Number of Groups: 5
>

Do you think this is good enough to demonstrate a learning effect.
Learning curves are exponential. I have been trying to log transform the response variable but then p-values are saying that previous experience has no significance.

>  mb<-lme(log.prodtime~Trial+Previous.experience+Trial*Previous.experience, data=  Data27_04, random=~1|Student, method="ML")
> summary(mb)
Linear mixed-effects model fit by maximum likelihood
Data: Data27_04
       AIC      BIC    logLik
  225.1042 248.9181 -104.5521

Random effects:
Formula: ~1 | Student
        (Intercept) Residual
StdDev:  0.04484554 0.495812

Fixed effects: log.prodtime ~ Trial + Previous.experience + Trial * Previous.experience
                               Value  Std.Error  DF  t-value p-value
(Intercept)                 4.448206 0.10593072 137 41.99165  0.0000
Trial                      -0.060150 0.02629765 137 -2.28726  0.0237
Previous.experience1       -0.333664 0.16351518   2 -2.04057  0.1781
Previous.experience2        0.368358 0.13776525   2  2.67381  0.1160
Trial:Previous.experience1  0.051714 0.04084708 137  1.26604  0.2076
Trial:Previous.experience2 -0.043036 0.03435150 137 -1.25282  0.2124
Correlation:
                           (Intr) Trial  Prvs.1 Prvs.2 Tr:P.1
Trial                      -0.886
Previous.experience1        0.248 -0.221
Previous.experience2       -0.237  0.209 -0.535
Trial:Previous.experience1 -0.220  0.266 -0.881  0.473
Trial:Previous.experience2  0.208 -0.225  0.474 -0.883 -0.551

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max
-2.7119095 -0.8005032  0.1127388  0.8621127  2.1988560

Number of Observations: 145
Number of Groups: 5
>

The model is surely better (AIC, BIC) also the residuals are looking better but then should I reduce the model leaving only the Trial number?

How would you present the results in a clear way? I am still struggling to figure it out. The concept of mixed models is clear in my head but it is hard to present it.

How should I then plot the learning curve?
I have been plotting the data I have adding a smooth line. Is this good enough?

Looking forward for your response
Best regards
Giovanna


Giovanna Ottaviani Aalmo
Stipendiat/Ph..D. Student
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