I am unclear about " I'm interested whether the selection of those choices had an impact on the outcome variable. " I thought the choice was the outcome variable.

Such models are called multivariate multilevel models

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#multipleresp

have a look at structures here

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#mlmbkgrd

Kelvyn Jones I'd like to explain: in the survey I asked respondents to choose 3 out of 10 best options that best describe their environment, and then in another question (the DV) I asked them to rate their satisfaction with the environment. Hence, the multiple choice explanatory variable is nest within the individual level and dv variable is at the individual level. Thanks for the links. I'll check it out now.

Am I correct to assume that I could have:

Level 1: 10 options

Level 2: DV satisfaction

I think you have a two level model - the higher level is the individual and the lower level are the multiple responses. I use the term higher and lower as some expositions use 1 and 0 and other 2 and 1. ( The reason for that discrepancy is that in a multivariate ml model, there is no covariance matrix at the lowest level.)

The data is usually observed and recorded in wide form with a line for each person. Here it would be an individual identifier and 10 response outcomes (say measured on a scale of 1 to 100), for each of these ten only 3 values would be observed and the other seven would be missing; variables measured on the individual level, here Sex each occupy another column as there is one observation per person

ID Resp1 Resp2 Resp3 ....... Resp10 Sex

1 67 42 * 32 M

2 12 28 96 * F

3 etc

This need to be reshaped into a long format so each individual gets 10 rows and the individual variable replicated, with the missing values preserved; thus

IdLong RespIndic RespL SexLong

1 1 67 M

1 2 42 M

1 3 * M

.........

1 10 32 F

2 1 12 F

2 2 28 F

..........

2 10 * F

3 1

Idlong is the level 2 identifier , and RespIndic is the level 1 identifier the latter could also be used to create the dummy predictor variables, I would recommend no intercept. RespL is the long staked response of all ten specific responses.

This stuff is not for the faint-hearted and you may have difficulty in estimation , especially of the higher-level covariances as you may have no information on some pairs - eg no individual chose response 6 and 7 as part of their three. It is worth doing a descriptive analysis first to find this out. Things will get even tougher if the response variables are not continuous.

I have no experience of SPSS but I think that these models could be estimated in Mplus and MLwiN. One of the golden rules of research design is that you plan in detail your data analysis the same time as you plan your data collection; not doing so makes things very tough. I too have been caught out. Things would have been easier if you had asked one relevant question of everybody, then you could have borrowed strength. Best of luck!

Kelvyn Jones Thank you for a detailed response. I have enrolled in the training to use MLwiN. I am truly thankful for your insight.

I have a cause of concern. When you say it would get tougher if the response variables are not continuous.... I wish to highlight that in fact the variables are not continuous on lowest level.

the 3 out of 10 choices (explanatory response variables) are in fact dichotomous, but the DV 'satisfaction' is recorded on a continuous scale on individual level. So the research question goes like this, which of the factors of environment if selected predict satisfaction for an individual in the given environment?

I've attached the figure to illustrate what I've understood from your explanation.

I am trying to figure out a way to reduce the number of response variables, i.e. 7 out of 10. e.g. in multiple regression the recommendation is that the dichotomous variable is not as dispersed as 1:9, so I could use the same rule of thumb to eliminate those conditions (out of 10) that were not selected at least 10% of the time, this could reduce the options.

The other option I am thinking of is using the format of combinations of 3 options as a new variable assigned to each case as Table 5 in this exercise https://joe.org/joe/2000june/tt2.php?fbclid=IwAR3as6sukexwajGm24Bb6HUQSVR3r_u6Tt6lv_uw7TCDjtxtLF8LvjrC1Qs

Let me know what you think.

Thank you for your patience and timely guidance.

I am lost! I think a lot of the confusion is coming about by the word response - when I use it , it means the dependent variable and not (as I think you are doing) an 'answer' to a question.

The wide to long data extract yesterday was to turn the data responses (that is multiple dependent variables ) to a single column with an indicator variable ( which could be turned into a set of dummies ). That is what I thought you wanted as you had pointed to the Andy Field example. To be clear, in these models the dependent variable is not at the higher level and replicated as it is in you posted extract, but at the lowest level.

If they are not multiple dependent variables then I think you are proposing to do the best thing that is recode them into different types of people according to their answers - you could then use standard multiple regression using the continuous dependent variable you have and specifying sets of dummies as the predictors to represent the types.

The stuff below is about dummy variable coding (there are lost of schemes) and dealing with interactions among dummies (that is 'combinations' of types of people).

https://stats.idre.ucla.edu/spss/faq/coding-systems-for-categorical-variables-in-regression-analysis/

https://www.theanalysisfactor.com/interaction-dummy-variables-in-linear-regression/

Kelvyn Jones

I get it. I've spent some time on your feedback. Thank you.

On pg 891-892 Tabachnick & Fidell, on Multi-level Modelling, give an example where on Level 1 there are three variables and only one of them is a dependent variable. However, in their example, all these three variables are measured at ratio scale.

Based on your feedback, my understanding is that in my data, each individual at level 1 is able to give a response to 10 dichotomous variables (environmental features) and one continuous/ratio variable (DV) (Satisfaction).

On level 2, i have a variable: location within room, 0/1 dichotomous, whether it is under a fan on or not

On level 3 i have a climate zone, e.g. categorical with 5 categories.

To correspond to Andy Field's example, (I am terribly sorry for the confusion), I have one additional variable in Level 1, which is not of the same type.

What I'm trying to ask now is whether this would be possible:

Level 1 is individual response to environment: 11 variables (10 dichotomous + 1 Continous DV)

Level 2 is Location within room) (1 dichotomous variable)

Level 3 is climate zone (5 climatic regions in the world)

We would start with checking if the satisfaction with the room is the same across all climates, then checking within buildings, whether the location wrt to fan affects the satisfaction, and then go on to see on level 1, how different environmental features as identified and perceived by the individual relate to satisfaction.

Thanks once again and a happy new year to you!