# Multiple imputation on single subscale item or subscale scores?

Recently I am conducting a research on the relationship between motivation/attitude variables (Gardner's model) and English language proficiency in the Philippines. I encountered a problem: missing values. I used a 160-item scale in my study, consisting of around 10 subscales, where each item has a 7-point Likert-type response set, with values from 1 to 7. Some respondents failed to answer some items.

I'd like to try "Multiple Imputation" using SPSS 18. But I have some questions, hope you can help out:

1. For example, the variable "Interest in foreign languages" is measured by a 10-item (Q1-Q10) scale, but some respondents left a few items unanswered. And again, "Attitudes toward English-speaking people" is measured by 8-item (e.g., Q11-Q18) scale. I wonder if I can impute missing values on a dataset with variable names such as, "ID, sex, age, Q1, Q2, Q3, Q4,...Q18, Final grade"? Or do I really have to add up the items first to get a subscale score before "Multiple Imputation"?

2. Do I have to recode those negatively worded items before "Multiple Imputation"? For example, if Q1, Q3, Q5, Q7, Q9 are negatively worded, do I have to recode them first?

3. It seems AMOS 18 cannot do "Calculate Estimates" on those imputed data. Do you think I should just average the five imputed values for each missing data to get a new value, from which I can build a new dataset so that AMOS 18 will have to handle only one complete dataset, rather than the five imputed datasets plus the original? Is averaging the five imputed values the right way of "POOLING"?

I basically concur with everything wolf.rauch said here, and would like to discuss some alternatives that might be available to you.

My understanding is that AMOS had had FIML (full information maximum likelihood) for continuous data for at least ten years before it was acquired by IBM -- see http://www.smallwaters.com/amos/faq/faqa-missdat.html, and that is an old FAQ by one of the original developers who left the project around 2000. If you are willing to ignore the ordinal nature of your items, you can just use this method, and won't bother figuring out multiple imputation.

If you don't like this solution, and you want to retain the categorical nature of the data, you would need to find the chained equations method with ordinal links (if SPSS has it at all). If SPSS only imputes draws from a multivariate normal distribution, then you are back to the situation of ignoring the ordinal nature of the data, and in no way better off than with AMOS' FIML. (I've no clue what's available in SPSS, you'd have to figure it out. In the end, everything would be fruitless if AMOS does not support multiple imputation -- and that, again, I don't know.)

If you are willing to consider Stata, there is a chance you'd be able to conduct your analysis in it, with all the bells and whistles of both multiple imputation for ordinal data using either Patrick Royston's ice or official mi, and then the new sem suite. Alternatively, you could run gllamm to obtain FIML estimates for ordinal data (although it would probably take eternity to converge).

Q1: I suppose you're not asking whether the variable names have anything to do with imputation. I suppose you're asking whether to do multiple imputation on your raw data or on "scales" which means sum scores of raw data variables which are assumed to measure the same construct.

Given that you are concerned about the right method (which is good), well, then how do you want to compute scale scores before you do anything about the missing data? Answer: you need to work with your raw data.

Q2: Multiple imputation works by estimating missing values from values of the other variables in your data set (this being a non-technical explanation). So it does not matter if you recode your variables or not, if by recoding you mean changing the sign of the relation from one var to the other variables. Still I would recommend recoding before the imputation so that you don't get confused afterwards.

Q3: I don't know why AMOS does not calculate estimates. I don't really know AMOS, but the user guide seems to say it should be able to calculate estimates for multiply imputated data sets. But there is a general answer anyway: The whole point of multiple imputation is that you get point estimates but also incorporate the additional variation introduced by the imputation process.

This means: You should not use a single "averaged" data set. Instead you work with all of your imputed data sets. First, you get point estimates for your model parameters by running your model (I suppose a structural equation model) for each of the data sets and taking the mean of the point estimates, and then you compute standard errors by combining between-imputation variance (variance of the parameter estimates between imputed data sets) with within-imputation variance (mean of the estimated standard errors from the different models). See any text on multiple imputation. A short and freely available tutorial is here: http://rhowell.ba.ttu.edu/Enders-MissingHancock.pdf

There's a great article comparing item-level vs. scale-level imputation by Craig Enders and colleagues (see here; sadly, one needs institutional access).

Basically, the authors conclude that both item-level and scale-level imputation are similar in the level of bias they introduce in scale estimates, but do differ in the efficiency (e.g., power), with scale-level imputation suffering a greater loss in power.