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I calculated duration (IV) in seconds using two different ranges (0 to 5s and 0 to 10s). The aim was to find out which range contributes to higher word learning outcomes (dichotomous DV).

I approached this in 2 ways:

Approach 1

I inserted data and scaled duration to have a data frame as follows:

Subject Word Score  Duration Range
1       1    0      -0.03    0to5
1       1    1       0.80    0to10
1       2    1      -0.93    0to5
1       2    0      -0.15    0to10
1       3    1       0.75    0to5
1       3    0       0.17    0to10

The number of Subjects and Word extend to 53 and 20 respectively. I run the "Range as factor" model of 2968 observations.

glmer(score~duration + Range + (1|Subject) + (1|Word),data= df,family='binomial')

As you see below, results showed that 0to10s range lowers scores by 0.46 (p = 0.04*). 

     AIC      BIC   logLik deviance df.resid 
  2347.8   2387.4  -1166.9   2333.8     2113 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.1945 -0.6678  0.2181  0.6278  3.1624 


Fixed effects:
                          Estimate Std. Error z value Pr(>|z|)  
(Intercept)                 0.5388     0.3101   1.737   0.0823 .
duration                    0.9457     0.4345   2.177   0.0295 *
range0to10                 -0.4597     0.2271  -2.025   0.0429 *
duration:Range0to10        -0.5851     0.3179  -1.840   0.0657 .
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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approach 2 Using filter function for Range levels, I split data into 2 data sets (0to5s data; and 0to10s data) and run separate models, each having 1060 observations.

Mod0to5s: glmer(score ~ duration + (1|Subject), data= 0to5data,family = 'binomial')
 AIC      BIC   logLik deviance df.resid 
  1252.7   1277.5   -621.4   1242.7     1055 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.6159 -0.7101  0.2650  0.6633  2.5760 
Fixed effects:
               Estimate Std. Error z value Pr(>|z|)  
(Intercept)      0.5423     0.3104   1.747   0.0806 .
   duration      1.1416     0.4913   2.324   0.0201 *



Mod0to10s: glmer(score ~ duration + (1|Subject), data= 0to10data,family = 'binomial')
AIC      BIC   logLik deviance df.resid 
  1248.0   1272.9   -619.0   1238.0     1055 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.7953 -0.7132  0.2689  0.6561  2.5497 
Fixed effects:
               Estimate Std. Error z value Pr(>|z|)    
(Intercept)    -0.08436    0.25928  -0.325 0.744896    
   duration    0.52693    0.15461   3.408 0.000654 ***

*10s model had the lowest AIC, hence, could probably be the best? But does AIC simply give the better fit and not necessarily whats the most better range for better scores? [which is exactly what I'm looking for in this pre-analysis stage]?

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AIC looks at variance explained while penalizing complexity of model by number of features used. If I'm understanding this correctly I think what you're seeing is when you merge the two the model is overall better, but I believe that's just because the model has more data to work with in approach two.

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  • $\begingroup$ I just want to know which range is conducive to better scores. Approach 1 says 10s is a better fit as duration improved scores (by 0.5 (p =0.0006***) in contrast to 7s model (by 1.1 but not as much sig p = 0.02*). Approach 2 shows 10s negatively affects outcomes. Which approach to go is still unclear to me $\endgroup$
    – Acer acer
    Commented Nov 19, 2019 at 15:02
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    $\begingroup$ Can you clean up your question by using consistent terminology (e.g., duration instead of range), explaining clearly the number of obsevations you used in each model and providing the output produced by R's summary() function applied to each model? Also, can you explain how it was possible for you to merge durations/ranges? It seemed from your first two models that duration was measured for the same study subjects, but differently? What are your study subjects, how many do you have in each of the three models and how exactly is duration defined in each model? $\endgroup$
    – Isabella Ghement
    Commented Nov 19, 2019 at 16:43
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    $\begingroup$ It might also help if you refer to the predictor duration as duration0to5 in model 1, duration0to10 in model 2, etc. $\endgroup$
    – Isabella Ghement
    Commented Nov 19, 2019 at 16:45
  • $\begingroup$ I improved the question as you suggested. Duration and range means two different things though. Duration was measured in a video for the same study subjects, but using 2 timespans/ranges (from 0 to 5s, and from 0 to 10s). This was done to decide on which range to adopt for the whole study (which range is conducive to better outcome). I have the same subjects with all models. $\endgroup$
    – Acer acer
    Commented Nov 19, 2019 at 18:13

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