[R-sig-ME] Linking a three level variable with a binary score to predict total score

[Johnathan Jones]

Hi all,

I am trying to analyse data from a listening perception experiment using
mixed models (suggested to me due to its ability to handle nested data).
New to mixed models, I have viewed several tutorials, but nothing quite
fits. I have a couple of things to work through, but the first is below.
I've tried numerous means of addressing the problem and have been going in
circles for longer than I'd like to admit. I'll avoid pasting the actual
data and results at this point as I expect less is more for clarity. Happy
to post more if it would help, however.



Explanation of the Problem

I have (what I'd like to be) a continuous dependent variable (DV = percent
correct of dichotomously scored items on a listening test, where 1 is
correct, 0 is incorrect) and several predictor variables. The key interest
is seeing how well listening accuracy with individual words (isolated
speech) predicts listening accuracy with sentences (connected speech).
Listening perception can be confounded by association (“Assn_status” in
Sample Data). If a word isn’t known or isn’t readily associated with the
context, it may be perceived as another word. Accurate perception is
further influenced by the listeners first language (L1). The equation would
be:

connected speech ~ isolated speech + association + L1 + 1|participant +
error

The snag is that association (categorical, three levels) is different for
each person, and I need to index the participants’ individual associations
for each item with their score on that item. It is unclear to me how to do
this, though I've tried what seems an infinite number of equally futile
options. It may be that I have to toss the idea of the continuous DV and go
with a logistic regression.


Sample Data (data = perception)

Participants from three language groups listened to sentences and
transcribed what they heard. Each sentence heard could reasonably include
one of two “target” words, as explained in the table notes under 1, 2 , and
3. The table below shows participant number (Participant), language (Lang),
item score (Score), the word that the participant associates with the
sentence (Assn), the actual word used in the audio (Key), whether the Assn
matches Key (Assn_status), overall performance on the isolated word task
(Isolated_prcnt)  and overall performance on sentence task (Cnncted_prcnt).
Assn and Key are included below for illustrative purposes to help explain
Assn_status.

*Partcpnt*

*Lang*

*Score*

*Assn*

*Key*

*Assn_status*

*Isolated_prcnt*

*Cnncted_prcnt*

1

Mandarin

1

beat

beat

same1

75

62.5

1

Mandarin

0

beat

bit

opposite2

75

62.5

1

Mandarin

1

beaten

beaten

same

75

62.5

1

Mandarin

0

beaten

bitten

opposite

75

62.5

1

Mandarin

1

meals

meals

same

75

62.5

1

Mandarin

0

meals

mills

opposite

75

62.5

1

Mandarin

1

none

risen

neither3

75

62.5

1

Mandarin

1

none

reason

neither

75

62.5

2

Mandarin

1

none

beat

neither

70

50

2

Mandarin

1

none

bit

neither

70

50

2

Mandarin

0

bitten

beaten

opposite

70

50

2

Mandarin

0

bitten

bitten

same

70

50

2

Mandarin

1

meals

meals

same

70

50

2

Mandarin

0

meals

mills

opposite

70

50

2

Mandarin

0

reason

risen

opposite

70

50

2

Mandarin

1

reason

reason

same

70

50

3

Mandarin

1

bit

beat

neither

85

75

3

Mandarin

1

bit

bit

neither

85

75

3

Mandarin

1

none

beaten

neither

85

75

3

Mandarin

1

none

bitten

neither

85

75

3

Mandarin

1

mills

meals

opposite

85

75

3

Mandarin

0

mills

mills

same

85

75

3

Mandarin

0

reason

risen

opposite

85

75

3

Mandarin

1

reason

reason

same

85

75

1The target word (key) is the same as the participant’s indicated
association with the sentence. For example, in “The man was ____”, a
participant may associate the word *bitten* more than *beaten* to complete
the sentence. If the audio was “The man was bitten”, the Assn_Status column
would indicate “same”.

2The target word in the item was opposite of the word the participant
associated with the sentence. If a participant associates *bitten* with the
sentence context, “The man was ___”, but the audio was, “The man was
beaten”, Assn_Status would indicate “opposite”.

3To the participant, both words have equal association to the given
context. There is no preference for one word over the other.


Attempts

Using the variables described in the Sample Data table and the nlme
package, I tried and failed with: model = lme(Cnnctd_prcnt ~ Language *
Isolated_prcnt, data = perception, random = ~ 1|Participant)
summary(model). While it ran and provided output, the resulting data
yielded different parameter estimates than the null model (LM), which
suggests failure somewhere, but I don't know where. My hope is that it will
seem obvious to someone here as is, but as noted previously, I'll happily
post the data if needed.

Related: Surprisingly (to me), the LM estimates were the same when using
either Score (a binary variable) or Cnnctd_prcnt (continuous) as the DV. It
seems R automatically aggregates the binary scores; am I accurate in
assuming this?  Would replacing Cnnctd_prcnt with Score be a suitable
workaround?


Thanks tremendously,


John Jones

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