# How to deal with non-questioned values in multiple regression?

## Background

I have a sample of customers, that I asked whether they had experience with different communication channels of a company (e.g. twitter, online shop, physical store, etc.).

For each communication channel they experienced I asked them to evaluate how satsified they were with their experience.

Finally I asked them to rate their overall satisfication with the company.

Determine the influence of each communication channel on the overall satisfaction via multiple regression.

## My problem

To due the questionnaire design not every person rated every communication channel, as most people do not experience all channels. However this creates missing data that I can not handle with simple listwise deletion as this would delete almost the complete sample.

## Solutions I tried

At the moment I can think of two ways to tackle this problem but I do not know a) which of these is better and b) how to do this completely:

1.) Treating missing values not as missing but rather as a viable value "Not experienced". This seems logical to me, since it can be assumed that not experience a communication channel is somewhat due to choice and says something about the overall satisfaction. However I do not know how to code this properly. by adding the value "Not experienced" do I treat the original ordinal satisfaction variable a nominal variable or would it be okay to treat the non-response as a lower value then 1 - Not satisfied at all?

2.) Imputing the missing values under the assumption that they are not MCAR. This seems difficult to me because every respondent has multiple variables with missing values instead of just one, so I do not know how to impute so many variables at once (e.g. for most respondents I would need to impute 5-8 variables out of 10).

Thank you all very much in advance.

This problem might be well-suited to hierarchical linear modelling, such that satisfaction is nested in channels. The way you describe your data, it might be organized in a "wide format:"

Participant  Satisfaction through Channel X  ...  Satisfaction through Channel j
1            1x                              ...  1j
2            2x                              ...  2j
...          ...                             ...  ...
i            ix                              ...  ij


The first step is to reformat your data into a "long format:"

Customer  Channel  Satisfaction
1         x        1x
.         .        .
.         .        .
.         .        .
1         j        1j
2         x        2x
.         .        .
.         .        .
.         .        .
2         j        2j
.         .        .
.         .        .
.         .        .
i         j        ij


In this format, missing data is less of a problem. With $overall$ as your outcome variable, $customer$ indexed as $i$, and $channel$ indexed as $j$, your mixed model for the hierarchical linear model would be:

$overall=\gamma_{00}+\gamma_{01}(channel_j)+\gamma_{10}(satisfaction_{ij})+\gamma_{11}(channel_j)(satisfaction_{ij})+e_{ij}+U_0+U_1$.

To determine the influence of each channel, you could compare the statistical significance of $\gamma$ parameters. Better yet, would be to add channels to your data in a stepwise manner to determine which channel reduces the variance of the $U_0$ and $U_1$ terms.

It might be tempting to just run the "long format" as a multiple linear regression, but you will have inflated type-I error rates because the nesting structure violates the assumption of independence.

For more information on this type of model, see Raudenbush & Bryk (2002).

• Wow, thanks for the great advice. I will certainly try your way because it looks promising. Just a couple of follow-up questions to understand everything: 1) Multiple linear regression is out, even if I go about it stepwise or even use something similar to shapely regression, correct? 2) I use SPSS, can you refer the package or analysis name I would have to use for analysis? – Fnguyen Dec 11 '17 at 9:40
• You can use multiple regression, but if the ICC is meaningful, you'll violate the assumption of Independence. There's a lot of smack talk about stepwise regression in my field, but I'm aware that's different for others. I've never heard of Shapley regression, so I can't comment. If you use normal multiple regression and the ICC is small, then I'd recommend contrast coding. I'm an R user, so I can't comment much on SPSS, but I believe it's the \MIXED command. – Jay Schyler Raadt Dec 11 '17 at 12:52
• wondering which R packages did you use for HLM? – Victor J Dec 13 '20 at 19:17