Choosing the Right Missing‑Data Method for SPSS Linear Regression on Moderately Sized Datasets

Problem and Decision

When you run a linear regression in SPSS on a moderately sized dataset (e.g., 200–500 cases) and some variables contain missing values, the analysis can fail or produce biased coefficients. The key decision is which missing‑data handling method to apply, given constraints such as sample size, missing‑data mechanism (MCAR, MAR), requirement for unbiased estimates, and SPSS version 28+.

Supported Options Overview

The following table summarizes the four methods that SPSS 28+ can use for linear regression with missing data.

Method	How it works	Sample size retained	Assumptions	Typical bias risk
Listwise (complete‑case) deletion	Removes any case that has a missing value on any variable used in the model.	Often < 50 % of original cases	Missing completely at random (MCAR)	High if data are not MCAR; can bias coefficients.
Pairwise deletion	Uses all available pairs for each predictor‑outcome combination; each regression may involve a different subset of cases.	Higher than listwise, but variable‑specific	Assumes MCAR for each pair; inconsistent across predictors	Unstable weights and incorrect standard errors.
Multiple Imputation (MI)	Creates m (≥5) completed datasets by iterative models (regression, hot‑deck, etc.), then pools results using Rubin’s rules.	Full sample size (≈ original N)	Missing at random (MAR) or MCAR	Low bias when imputation model is correctly specified.
Expectation Maximization (EM)	Directly maximizes the likelihood for linear models under MAR, avoiding explicit imputation steps.	Full sample size	MAR (EM works best for linear models)	Potential convergence issues; limited to models that support EM.

Trade‑off Analysis

Listwise deletion is the simplest but often wastes too many cases, especially when missingness is not MCAR. Pairwise deletion can inflate the number of usable observations but breaks the assumption of a single analytic sample, leading to inconsistent estimates. MI preserves power and provides valid standard errors when the imputation model matches the substantive model; however, misspecifying the imputation (e.g., using a linear model for a categorical predictor) can introduce bias, particularly in small samples. EM estimation avoids the imputation step and yields efficient estimates under MAR, but it is only available for certain variable types and may fail to converge if the model is poorly specified or if data are MNAR.

Concrete Implementation: Multiple Imputation in SPSS

Below is a step‑by‑step guide to run MI for a linear regression using SPSS 28+. The example assumes a dataset named survey.sav with variables age, income, and education, where income has missing values.

1. Open Analyze → Missing Value Analysis.
2. Select the variables (age, income, education) and click Statistics.
3. Choose Expectation Maximization as the estimation method and set Number of imputations to 5 (the minimum recommended).
4. Click Continue, then OK to start the imputation.

After the imputation completes, SPSS creates five new data files (e.g., survey_1 imputed.sav to survey_5 imputed.sav).

To run the regression on each imputed dataset:

TITLE LIST.
REGRESSION
  /DEPENDENT income
  /METHOD=enter age education.

Repeat the REGRESSION command for each of the five files. SPSS will store the output in the active spreadsheet.

Finally, combine the results:

1. Go to Analyze → Multiple Imputation → Combine Subgroup Results.
2. Select the five regression outputs (they appear as separate “subgroup” entries).
3. Click OK. SPSS produces a single set of coefficients, standard errors, t‑values, and confidence intervals that reflect Rubin’s rules.

Verification steps:

• Check the Missing Values Analysis dialog for convergence diagnostics (e.g., change in log‑likelihood) before trusting EM‑based estimates.
• Inspect the imputed values for extreme patterns; use Graphs → Histogram for each variable to ensure plausibility.
• Compare the pooled coefficients with those from a complete‑case analysis to gauge bias.

When to Prefer EM over MI

If your regression model is purely linear and all predictors are continuous, EM can be more efficient because it avoids the extra iteration required for imputation. However, you must:

1. Confirm that the model is MAR (or MCAR) for the variables involved.
2. Run the Missing Values Analysis dialog, select Expectation Maximization, and verify that the Convergence criterion meets the default tolerance (≤ 0.001).
3. Be aware that EM is not available for mixed‑type models or for interactions that involve categorical variables unless you expand the model specification.

Risk: if the EM algorithm fails to converge, the resulting coefficients may be unreliable; in that case fall back to MI.

Practical Check of the Result

After obtaining pooled estimates, run a simple diagnostic:

1. Compute the R‑squared for each imputed regression; the pooled R‑squared should be close to the average across imputations.
2. Plot the residuals of the pooled model (use GRAPH /SCATTERPLOT) to check for systematic patterns that could indicate model misspecification.
3. If the proportion of missing cases exceeds 10 % in any key variable, consider collecting more data or adjusting the measurement instrument before relying on any single method.

Summary of Recommendations

For a moderately sized dataset where missingness is suspected to be MAR, Multiple Imputation is the most balanced choice: it retains full sample size, provides unbiased coefficients, and yields correct standard errors when the imputation model is appropriate. Use Listwise deletion only when missingness is truly MCAR and the resulting sample would still be sufficiently large. Pairwise deletion should be avoided for inferential statistics because of its inconsistency. EM is a viable alternative for pure linear models with MAR data, but requires careful convergence checking.

Key Takeaway

Choosing the right missing‑data method in SPSS hinges on the missing‑data mechanism and the need for unbiased, efficient estimates. When in doubt, run a Missing Values Analysis, try MI with at least five imputations, and validate the pooled results against a complete‑case benchmark.