might be a useful link for you

https://stats.stackexchange.com/questions/255106/combining-multiple-likert-scale-variables-into-a-new-single-variable

Thank you Gayatri for the link. However, I do not mean combining variables measured on different scales. In my scenario, each respondent evaluated 24 statements for 5 different brands (from 0 strongly disagree to 10 strongly agree). Now I need one set of 24 statements, which would include valuations for all brands to run factor analysis. 

Hi Davit,

It sounds like you need to transform your data into a different shape to conduct the analysis you are suggesting.  I am guessing that your data currently looks like this (but please correct me if I am wrong)...

id     prod1_q1     prod1_q2     prod1_q3     .....     prod2_q1     prod2_q2   ....     etc..

1            3                     4                    6                                4                   2

2            4                     5                    3                                5                   3

3            6                     5                    5                                5                   4

(I think this is what you are describing - a grid consisting of a row per respondent and 5*24 variables (i.e. columns)

What I think you need is to simply create a new data frame which adds an extra variable called something like "product", which denotes whatever product you are referring to (i.e. a number from 1 to 5), and then create a grid with 5 rows per respondent with a separate row for each product (in a sense, you are then creating a combined id-product identifier) - so it would look a bit like this:

id     product              q1                  q2     .....   etc..

1            1                     3                    4                             

1            2                     4                    2                               

1            3                     6                    9                            

1            4                     3                    4                             

1            5                     4                    2                               

2            1                     6                    9                            

2            2                     3                    4                             

2            3                     4                    2                               

2            4                     6                    9                            

Hope this helps

Tony

Dear Tony,

Thank you for your comment

You are right and data looks the same as you have described. In addition, I have a variable “brand” showing which brand the consumers choose very often (from 1 to 5). Can I use this variable as a product identifier or simply create another variable that you suggested. If I understand correctly, I have to indicate id & brand as product identifiers before restructuring, right?

For ex:

Id     brand_consump.     brand                  q_1        …………..

1              2                             1                       3             

1              2                             2                       8

1              2                             3                       3

1              2                             4                       2

1              2                             5                      10

Moreover, in my data I have missing values (99). What can I do with them? Different approaches have been suggested like either delete each case with missing values or replace with the average score for each variable. What do you suggest? Personally, I think deleting cases would be much better scenario rather than replacing with average scores.

I plan to run Factor analysis (principal component) to determine factors that define brand image and then use regression to understand, which factors influence on the positive image of brand. Dependent variable is to what extent consumers like each brand measured on scale 0 totally dislike and 10 totally like. Can I use linear regression in this case? 

Thank you for your contribution

It is highly appreciated

Davit

Dear Davit,

Essentially transforming the data allows you to treat the choices people make as if they were independent (for the purposes of a principle components analysis). Once you create "long" data like this, you can add in as many variables as you like - as long as those variables that are singular for each id are repeated as appropriate (which is exactly what you have done in your example).

Regarding missing values, it is hard to know what to advise without knowing more about your data - how many respondents do you have? Do some respondents have high levels of missingness, or is the missing data distributed fairly randomly across your sample? My usual preference would be to use list-wise deletion, but as I say, it very much depends on your data. If for example someone simply fails to fill in the survey for one product, but has full data for the other 4, it would seem like a shame to throw away the data you do have, so you could deal with missing data on a product-by-product basis in this case.

What process do you intend to use following the factor analysis? Are you looking for clusters of variables in an exploratory manner, in order to combine them in a scale-like manner (e.g. taking the mean after checking the cronbach's alpha, etc..), or are you intending to use the factor loadings themselves?

You have a choice whether to keep the data in long form when you carry out the follow-up analysis, but you need to be careful to remember that this form of data (unless you include the id variable in your analysis - as you might with a mixed model for example) does not treat each row as a respondent (obviously). To carry out a simple regression, it might be more straightforward to reshape the data again back to "wide" form (after the PCA) and then run the analysis with rows as respondents. It kind of depends what your plan is, and also on what software you are using.

If 'liking' is your dependent variable, then I assume it is not included in the PCA. If it is an independent measure, then yes - a linear model would seem like a reasonable choice.

All the best

Tony

Dear Tony,

Thank you again for your interest and contribution

Regarding missing data:

In total, I have 2000 respondents. Before restructuring  my data, I have checked missing data distribution by using “missing data analysis option in SPSS. In some statements the missing values have been highly concentrated. I have excluded missing values from all statements including dependent variable listwise and as a result I got 627 respondents without any missing values.  What do you think about this strategy?  

my research questions:

1.       What are the factors that influence brand image (all brands together)? What is the relative importance of those factors (interested in weights)? 

Firstly, I plan to run Factor analysis (Principal Component) to identify factors (in total I have 24 variables after restructuring the data, where each respondent is replicated 5 times). Then, I plan to run OLS and regress my factors with dependent variable measuring to what extant consumers like specified brands (measured with 0 strongly dislike and 10 strongly like). Then, I plan to define relative importance of each factor by using squared t statistics since it does not impose distortions compared to standardized beta coefficients.

There is some disagreement regarding likert data to treat it as ordinal or interval. In my case, I have statements from strongly disagree to strongly agree with clear cut point between positive and negative directions. Dependent variable measuring likeness of each brand (0 strongly dislike to 10 strongly like). So, I treat them as scale data. For OLS, procedure I need dependent variable to be metric and normally distributed. I have checked “skewness and kurtosis” for my dependent variable and this is result. Rule of thumb here is the following:

If skewness is less than −1 or greater than +1, the distribution is highly skewed.

If skewness is between −1 and −½ or between +½ and +1, the distribution is moderately skewed.

If skewness is between −½ and +½, the distribution is approximately symmetric.

In my case "skewness" is -0.968 < -1 means that distribution of my dependent variable is moderately skewed left. 

What can you say about this result? 

                Statistics - h2 

 N        Valid                         3135 

            Missing                          0

Skewness                              -.968

Std. Error of Skewness       .044

Kurtosis                                  .888

Std. Error of Kurtosis            .087

Then I would like to regress factors on each brand separately. Do I have to convert variable brand_con. Into dummy and use binary logistic?  

Your comments are highly appreciated

Best regards,

Davit

Hi Davit,

I am not a statistician (my main expertise is in environmental psychology), so my detailed expertise is limited in these matters, so I would advise consulting a statistician on some of these questions. However, as far as I understand it, I think the normality issue is mostly important in terms of the regression model residuals as opposed to the input variables.  Some skew is pretty much always present in data like these.  In the first instance, I would suggest running a basic OLS regression (and checking the normality of the residuals), and examining the model outcome.  Once you have done this, you can then refine the model if appropriate.  If you are concerned about the spacing between responses potentially not being equal (i.e. is the distance between a '1' and '2' different than the difference between a '2' and a '3' response), then you could consider using an ordinal regression model, but if you go down this track, I would certainly recommend consulting a statistician - they are worth their weight in gold!

Cheers

Tony

Dear Tony, 

Thank you for your recommendations and follow up. 

One last question, regarding restructuring my data. I tried two scenarios. In the first case, I have deleted missing data and then restructured. In this case, I got in total 627 cases. In the second scenario, first I restructured data and then deleted missing values. In the second case, I got 798 cases without missing data, however, in some cases each respondent is no longer replicated 5 times since I deleted missing data. I have something likes this 

id                brand                 q_1         q-2     ............

1                   1

2                   1

2                   2 

2                   3

2                   4

2                   5 

Will this create a problem in factor or regression analysis ? 

Thanks a lot 

Best regards 

Davit 

I think the safest thing to do would be to delete the missing data first, and then restructure (i.e. the option resulting in 627 cases).

Dear Tony, 

Do you have in mind any paper that has used similar data structure (transformed) for factor analysis? 

Thanks 

Davit 

no - I do not have any particular paper in mind.  If the purpose of the PCA is to explore the structure of the responses, then I see no reason for this to be problematic.  If however you are looking for a method that somehow takes into consideration the within-respondent variability, then i am afraid I do not know how to do this.

Dear Tony, 

In your earlier comments you mentioned the following: 

"Essentially transforming the data allows you to treat the choices people make as if they were independent (for the purposes of a principle components analysis)". So, it means that in case of restructuring, I treat answers from each respondent for five different brands as independent even though respondents replicate, right? 

Best regards, 

Davit 

yes - for the purposes of the PCA, if you take this approach, you would be treating the responses as if they were independent.  Clearly they are not independent in reality, but I don't think it is problematic to treat them as such when conducting a PCA (but this is an aspect you should probably check with a statistician). Because you want to compare between different brands, but first want to explore the latent structure of the response variables, you need to first look at all of the response data ignoring the brands that have generated them, and (I think) the only simple way to do that is to basically stack up all of the data and focus the analysis on the responses themselves.