Abstract
Missing data in a field experiment may arise from a number of sources. Participants may skip over questions inadvertently or refuse to answer them; they may offer an illegible response; they may fail to complete a questionnaire; or they may be absent from an entire measurement session in a longitudinal study. The last is often called wave nonresponse. Many participants who are unavailable for one or more occasions of measurement are available at later occasions. We define attrition is a special case of wave nonresponse in which a participant drops out of a study after a certain time and is no longer available at any subsequent wave of data collection.
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Notes
- 1.
This last step involved a simple trial and error process: Try a particular sample size; if the SE was too large, increase the sample size and try again.
- 2.
The MGSEM procedure makes use of the covariance matrix as input. When the covariance matrix is analyzed in this manner, one may simply change the sample size indicated in model being tested without changing the input covariance matrix. The more commonly used FIML approach cannot do this. With that approach, raw data must be input. And with raw-data input, the sample size is tied directly to the data being input (e.g., with N = 500, 500 cases are read from the raw data file). Thus with the FIML methods, changing the sample size changes the data being read, thereby producing changes in the results.
- 3.
One can safely ignore the “W_A_R_N_I_N_G” in the LISREL output that “LAMBDA-Y does not have full column rank”. It is a necessary byproduct of this analysis.
- 4.
We chose r XY = .10 because the issue of N EFF becomes most important with small effect sizes. This is closely related to the issue of determining statistical power with varying effect sizes. With large effect sizes, especially in field experiments, it is often possible to find significant effects, even with relatively small sample sizes. It is often the case that sample size is an issue only with smaller effect sizes. We address the issue of other values of rXY later in this chapter.
We arbitrarily chose r XZ = .10. In our experience, this value always tends to be rather similar to r XY. We address the issue of different values of r XZ later in this chapter.
- 5.
This is true unless the variables acting as auxiliary variables happen to be part of the analysis model. The only analysis that fits this requirement well is growth modeling. That is, even when there are missing values in the growth part of the model, the growth model can be estimated making use of partial data. Although the results of this analysis are not maximum likelihood, they do tend to be unbiased and efficient.
- 6.
For this demonstration, we will stay with the scenario in which N TOT = 1,000, N CC = 500, and %Z = 100 % for both auxiliary variables.
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Graham, J.W., Collins, L.M. (2012). Using Modern Missing Data Methods with Auxiliary Variables to Mitigate the Effects of Attrition on Statistical Power. In: Missing Data. Statistics for Social and Behavioral Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4018-5_11
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