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2 x (2) design with binary-->continuous within-subject variable

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ac11ca

2 x (2) design with binary-->continuous within-subject variable

Hi there,

I am hoping that you might be able to help me analyse some data from a
decision-making experiment I ran recently.

I have a 2 x (2) design where the within-subjects measure variable changes
from a binary response (i.e., 0,1) to a continuous response (i.e., 0-100). I
realise that this is very odd, but it is central to my current research
question: Are people more like to prefer a risky gamble over a safe gamble if
the choice is presented as a single play or the accumalted sum of 100 plays?

My data looks like this in SPSS (Note: Format = between-subjects categorical
IV [coded 1,2] and Plays = within-subjects categorial IV [coded 1,2], and
Choice = DV that is half the time binary [0,1] and half the time continuous[0-100]):

ID Format Plays Choice
1 1 1 0.00
1 1 2 0.15
1 2 1 1.00
1 2 2 0.78
.
.
.
.
93 1 1 0.00
93 1 2 0.01
93 2 1 1.00
93 2 2 0.97

I started by analysing my data with a mixed ANOVA and found an interaction,
which is what I was hypothesising. Of course, one of the assumptions of the
ANOVA is that the data are normally distributed, which they clearly are not
with my binary response data.

To get around this problem I conducted a repeated measures logistical
regression using the SPSS Generalised Estimating Equations function (GEE)
under a binary model type. However, the GEE method accepts only one
distribution for my within-subjects variable: binomial or scale responses. If
I chose scale, then I am just running an ANOVA (I think!). If chose binomial,
then I have to convert the continuous DV to a binary DV (and cut all 50/50
responses), which basically undermines the motivation of the experiment and
eliminates crucial differences.

Thus, I think that I must use the original mixed ANOVA analysis and produce
some hand-waving sort of justifcation. I was wondering if anyone might be
able to help me with this justification. For example, what is the impact of
having a binary DV in the middle of a mixed ANOVA and is it really so bad?

Thanks for any help that you might be able to provide. If anyone wants to see
the data, feel free to email me at ac11ca[at]hotmail[dot]com.

Cheers,
Adrian

Maguin, Eugene

Re: 2 x (2) design with binary-->continuous within-subject variable

Adrian,

I don't know how to analyze this but I'm curious about the study design. How
did the design work? Do you present them with a scenario but vary the
outcome likelihood information such that in one condition you say
'likelihood of success is x' and in the other condition you say the
'likelihood of success is 'y out of 100' where y=100*x. And while x varies
over persons, x and y/100 are the same for both of a person's trials? The
person then makes a yes/no decision?

If so, it would seem like the null hypothesis is that the two plotx of
proportion of yeses by likelihood of success should be coincident or, more
correctly, be not different.

Gene Maguin

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
ac11ca
Sent: Saturday, September 24, 2011 11:13 PM
To: [hidden email]
Subject: 2 x (2) design with binary-->continuous within-subject variable

Hi there,

I am hoping that you might be able to help me analyse some data from a
decision-making experiment I ran recently.

I have a 2 x (2) design where the within-subjects measure variable changes
from a binary response (i.e., 0,1) to a continuous response (i.e., 0-100). I
realise that this is very odd, but it is central to my current research
question: Are people more like to prefer a risky gamble over a safe gamble
if
the choice is presented as a single play or the accumalted sum of 100 plays?

My data looks like this in SPSS (Note: Format = between-subjects
categorical
IV [coded 1,2] and Plays = within-subjects categorial IV [coded 1,2], and
Choice = DV that is half the time binary [0,1] and half the time
continuous[0-100]):

ID Format Plays Choice
1 1 1 0.00
1 1 2 0.15
1 2 1 1.00
1 2 2 0.78
.
.
.
.
93 1 1 0.00
93 1 2 0.01
93 2 1 1.00
93 2 2 0.97

I started by analysing my data with a mixed ANOVA and found an interaction,
which is what I was hypothesising. Of course, one of the assumptions of the
ANOVA is that the data are normally distributed, which they clearly are not
with my binary response data.

To get around this problem I conducted a repeated measures logistical
regression using the SPSS Generalised Estimating Equations function (GEE)
under a binary model type. However, the GEE method accepts only one
distribution for my within-subjects variable: binomial or scale responses.
If
I chose scale, then I am just running an ANOVA (I think!). If chose
binomial,
then I have to convert the continuous DV to a binary DV (and cut all 50/50
responses), which basically undermines the motivation of the experiment and
eliminates crucial differences.

Thus, I think that I must use the original mixed ANOVA analysis and produce
some hand-waving sort of justifcation. I was wondering if anyone might be
able to help me with this justification. For example, what is the impact of
having a binary DV in the middle of a mixed ANOVA and is it really so bad?

Thanks for any help that you might be able to provide. If anyone wants to
see
the data, feel free to email me at ac11ca[at]hotmail[dot]com.

Cheers,
Adrian

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nuous-within-subject-variable-tp4837785p4837785.html
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Ryan

Re: 2 x (2) design with binary-->continuous within-subject variable

In reply to this post by ac11ca

You need to better describe the administration of the experiment. It
looks like you have four measurements for each subject, two of which
are binary and two are bounded between 0 and 100. Is that correct?
Please provide a concrete example of how this experiment was
administered to a single subject. A step-by-step explanation would be
helpful (i.e., subject is presented with x and responded with x, then
subject is presented with x and responded with x, etc.). It isn't
clear to me, for instance, how the first subject in your dataset
illustration obtained a value of 0.15 (second case in your dataset).

Ryan

On Sat, Sep 24, 2011 at 11:13 PM, ac11ca <[hidden email]> wrote:

> Hi there,
>
> I am hoping that you might be able to help me analyse some data from a
> decision-making experiment I ran recently.
>
> I have a 2 x (2) design where the within-subjects measure variable changes
> from a binary response (i.e., 0,1) to a continuous response (i.e., 0-100). I
> realise that this is very odd, but it is central to my current research
> question: Are people more like to prefer a risky gamble over a safe gamble
> if
> the choice is presented as a single play or the accumalted sum of 100 plays?
>
> My data looks like this in SPSS (Note: Format = between-subjects
> categorical
> IV [coded 1,2] and Plays = within-subjects categorial IV [coded 1,2], and
> Choice = DV that is half the time binary [0,1] and half the time
> continuous[0-100]):
>
> ID Format Plays Choice
> 1 1 1 0.00
> 1 1 2 0.15
> 1 2 1 1.00
> 1 2 2 0.78
> .
> .
> .
> .
> 93 1 1 0.00
> 93 1 2 0.01
> 93 2 1 1.00
> 93 2 2 0.97
>
> I started by analysing my data with a mixed ANOVA and found an interaction,
> which is what I was hypothesising. Of course, one of the assumptions of the
> ANOVA is that the data are normally distributed, which they clearly are not
> with my binary response data.
>
> To get around this problem I conducted a repeated measures logistical
> regression using the SPSS Generalised Estimating Equations function (GEE)
> under a binary model type. However, the GEE method accepts only one
> distribution for my within-subjects variable: binomial or scale responses.
> If
> I chose scale, then I am just running an ANOVA (I think!). If chose
> binomial,
> then I have to convert the continuous DV to a binary DV (and cut all 50/50
> responses), which basically undermines the motivation of the experiment and
> eliminates crucial differences.
>
> Thus, I think that I must use the original mixed ANOVA analysis and produce
> some hand-waving sort of justifcation. I was wondering if anyone might be
> able to help me with this justification. For example, what is the impact of
> having a binary DV in the middle of a mixed ANOVA and is it really so bad?
>
> Thanks for any help that you might be able to provide. If anyone wants to
> see
> the data, feel free to email me at ac11ca[at]hotmail[dot]com.
>
> Cheers,
> Adrian
>
>
> --
> View this message in context: http://spssx-discussion.1045642.n5.nabble.com/2-x-2-design-with-binary-continuous-within-subject-variable-tp4837785p4837785.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>

=====================
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ac11ca

RE: 2 x (2) design with binary-->continuous within-subject variable

In reply to this post by Maguin, Eugene

Hi Gene,

Thanks for your interest. The design was as follows:

All participants faced a binary gamble between a safe option and a risky option. For example, a 100% chance of $3 vs. an 80% chance of $4, else nothing.

Each participant had to make two choices. First: which option do you prefer if the gamble will be played once? Second: how would you allocate 100 plays between the two options assuming you recieve the sum of all realised outcomes?

Participants in the "description" group learnt about the pay off distribution of the two options from a summary description much like the one presented above.

Participant in the "experience" group learnt about the pay off distribution of the two options from a process of sequentially sampling 40 individual outcomes that corresponded to a distribution equivalent to the description (e.g., 4,4,0,4,4,4,4,0,4,4....... vs. 3,3,3,3,3,3,3,3,3,3,3).

Thus, the design is a 2 x (2) study. The between subjects variable is choice format (description vs. experience). The within subjects variable is how many times the gamble will be played (x1 or x100).

The research question: Are people more like to prefer a risky gamble over a safe gamble if the choice is presented as a single play or the accumalted sum of 100 plays (and does it matter if the gamble is learnt from description or by experience)?

Cheers,
Adrian

Date: Sun, 25 Sep 2011 17:00:04 -0700
From: [hidden email]
To: [hidden email]
Subject: Re: 2 x (2) design with binary-->continuous within-subject variable

Adrian,

I don't know how to analyze this but I'm curious about the study design. How
did the design work? Do you present them with a scenario but vary the
outcome likelihood information such that in one condition you say
'likelihood of success is x' and in the other condition you say the
'likelihood of success is 'y out of 100' where y=100*x. And while x varies
over persons, x and y/100 are the same for both of a person's trials? The
person then makes a yes/no decision?

If so, it would seem like the null hypothesis is that the two plotx of
proportion of yeses by likelihood of success should be coincident or, more
correctly, be not different.

Gene Maguin

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
ac11ca
Sent: Saturday, September 24, 2011 11:13 PM
To: [hidden email]
Subject: 2 x (2) design with binary-->continuous within-subject variable

Hi there,

I am hoping that you might be able to help me analyse some data from a
decision-making experiment I ran recently.

I have a 2 x (2) design where the within-subjects measure variable changes
from a binary response (i.e., 0,1) to a continuous response (i.e., 0-100). I
realise that this is very odd, but it is central to my current research
question: Are people more like to prefer a risky gamble over a safe gamble
if
the choice is presented as a single play or the accumalted sum of 100 plays?

My data looks like this in SPSS (Note: Format = between-subjects
categorical
IV [coded 1,2] and Plays = within-subjects categorial IV [coded 1,2], and
Choice = DV that is half the time binary [0,1] and half the time
continuous[0-100]):

ID Format Plays Choice
1 1 1 0.00
1 1 2 0.15
1 2 1 1.00
1 2 2 0.78
.
.
.
.
93 1 1 0.00
93 1 2 0.01
93 2 1 1.00
93 2 2 0.97

I started by analysing my data with a mixed ANOVA and found an interaction,
which is what I was hypothesising. Of course, one of the assumptions of the
ANOVA is that the data are normally distributed, which they clearly are not
with my binary response data.

To get around this problem I conducted a repeated measures logistical
regression using the SPSS Generalised Estimating Equations function (GEE)
under a binary model type. However, the GEE method accepts only one
distribution for my within-subjects variable: binomial or scale responses.
If
I chose scale, then I am just running an ANOVA (I think!). If chose
binomial,
then I have to convert the continuous DV to a binary DV (and cut all 50/50
responses), which basically undermines the motivation of the experiment and
eliminates crucial differences.

Thus, I think that I must use the original mixed ANOVA analysis and produce
some hand-waving sort of justifcation. I was wondering if anyone might be
able to help me with this justification. For example, what is the impact of
having a binary DV in the middle of a mixed ANOVA and is it really so bad?

Thanks for any help that you might be able to provide. If anyone wants to
see
the data, feel free to email me at ac11ca[at]hotmail[dot]com.

Cheers,
Adrian

--
View this message in context:
http://spssx-discussion.1045642.n5.nabble.com/2-x-2-design-with-binary-conti
nuous-within-subject-variable-tp4837785p4837785.html
Sent from the SPSSX Discussion mailing list archive at Nabble.com.

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

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Ryan

Re: 2 x (2) design with binary-->continuous within-subject variable

In reply to this post by ac11ca

Adrian,

You have a bivariate response for which the distribution of the first
variable is binary (safe vs. risky) and the distribution for the
second variable could be binomial (# of risky events / 100) or perhaps
more accurately beta (continuous variable bounded between 0 and 100
risky events). Regardless, a model which accounts for within-subject
correlation between the bivariate responses is warranted. As far as
I'm aware, SPSS does not have a procedure which accommodates a
bivariate response model when the distributions of the response
variables are different. SAS is certainly capable of handling this
type of model. I still have a few questions about your study, but
thought I'd just give you my initial reaction.

Ryan

On Sat, Sep 24, 2011 at 11:13 PM, ac11ca <[hidden email]> wrote: