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Multilevel and time-series missing value imputation for combined survey and longitudinal context data

Abstract

Comparative research examining relationships between individual-level survey response data and time-varying country context variables for political or socioeconomic characteristics is often complicated by missing values. Surveys and longitudinal context measures may be produced during alternative years and at differing frequencies. Observations may be intermittent or may only cover few consecutive years across a full longitudinal sequence. Statistical evaluations that do not impute values with consideration to data’s missingness characteristics may produce biased estimates. Model-based approaches for missing value imputation such as multiple imputation and time series imputation offer means through which imputed values may be produced given complex hierarchical and longitudinal relations. Using incomplete survey data for institutional trust measures from 554,104 respondents from twenty-seven Eastern European and Central? Asian countries between 1993 and 2016, and corresponding longitudinal context descriptors of demographic, socioeconomic and political conditions, multilevel multiple imputation and time-series imputation methods were compared and evaluated. Where missingness is intermittent across the breadth of longitudinal sequence, time series imputation may produce convincing estimates for national-level variables’ values while understating uncertainty associated with imputation. When missing values are numerous and span tail ends of a sequence, multivariate multilevel multiple imputation with time variable fixed effects may produce better estimates for country-variables through incorporation of information derived from additional covariates and other countries’ concurrent trajectories. Multilevel multiple imputation models with random slopes for time variables were found to have beneficial qualities in that countries’ unique longitudinal trends are emphasized and fit while that effects of pooled observations and additional covariates contribute to estimation.

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Notes

  1. 1.

    For example, within the regions of Eastern Europe and West Asia, measurement and public release of several economic and demographic characteristics began in large part with the 1990s. Only since the 2000s has the report of context characteristic data largely increased in frequency and regularity within the countries of Central and Southwest Asia and Southeast Europe.

  2. 2.

    These countries are Albania, Armenia, Belarus, Bosnia-Herzegovina, Bulgaria, Croatia, Czech Republic, Estonia, Georgia, Greece, Hungary, Kazakhstan, Kyrgyzstan, Latvia, Lithuania, Macedonia, Moldova, Poland, Romania, Russia, Serbia, Slovakia, Slovenia, Tajikistan, Turkey, Ukraine and Uzbekistan.

  3. 3.

    The programs were the World Values Survey, the Caucasus Barometer, Consolidation of Democracy in Central and Eastern Europe, European Quality of Life, European Social Survey, European Values Study, Life in Transition, New Baltic Barometer, the New Europe Barometer, the New Russia Barometer, Values and Change in Post-communist Europe and the Asian Barometer.

  4. 4.

    Approaches’ prediction matrices used within the mice imputation function are further defined in Appendix B.

  5. 5.

    When conducting univariate time series imputation, Poland and Serbia’s longitudinal sequences for the poverty rate had zero observations. In such a case, the univariate time series method has no data to draw upon and no imputations could be performed. As such, yearly mean values of the complete imputed poverty rate variable across the other twenty-five countries were used to generate estimates for the two countries’ yearly poverty rate values.

  6. 6.

    Countries with no observations for a variable were not considered.

  7. 7.

    The missing data pattern for the combined two-level data is described in Appendix A.

  8. 8.

    A preliminary complete case analysis of associations between poverty rate and all other considered longitudinal context and survey respondent covariates through use of a multilevel model with random effects found all independent variables except respondent age to be significantly associated with a country’s yearly poverty rate.

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Funding

This work was supported in part by funding from a Fonds de recherche du Quebec – Société et culture (FRQSC) doctoral research scholarship.

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Correspondence to David Wutchiett.

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Appendices

Appendix A

See Appendix Fig. 

Fig. 6
figure6

Missingness pattern within combined country-level and individual-level data Variables for “Country”, “Year”, “Year^2”, “Partial Democracy”, “Autocracy” and “Regime in Transition” were not missing for any observation and were not included in missingness pattern plots. Variables “Trust Parl” for trust in parliament/congress, “Female”, “Age” and “Education” are survey respondent variables. The other variables described socioeconomic and political context characteristics. Missingness is measured on a scale of 0 to 1

6.

Appendix B Multiple imputation model prediction matrices in mice R package format

See Appendix Table

Table 4 Multiple imputation prediction matrix for multilevel model with country random effects (ML RE) approach

4,

Table 5 Multiple imputation prediction matrix for multilevel models with longitudinal variable random slopes (ML RS) approach

5 and

Table 6 Multiple imputation prediction matrix for second step multilevel model with random effects for survey respondent variables of the two-step imputation (TS + ML RE) approach

6

Within the prediction matrices, rows with only zero values are not imputed whereas those with the other numeric values describe the model specifications in regard to the columns’ variables. Context variables are consistently defined across approaches with fixed effects. Individual survey respondent variables are defined with fixed effects with an additional country cluster-specific mean value fixed effect. As populations randomly sampled for public opinion surveys within a country would tend to continue to largely exist across years and retain similar characteristics in terms of their distributions, generating a mean value variable for individuals’ demographics used during imputation enables the modeling approach to take into account the accumulated information about a country’s population. Since values for context measures are expected to vary more considerably over time, departing from sequentially adjacent observed values, the addition of country means would tend to reduce the effect size associated with variables included to introduce model adjustments to fit context variables’ variation across longitudinal sequences. Since increasing sensitivity to time trends was a central goal, these additional country means were not included.

For approach two, the year components are set to random slopes whereas they are defined as fixed effects for approaches one and three. These prediction matrices defined as R data frame objects were used within the ‘mice’ function during the multiple imputation process.

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Wutchiett, D., Durand, C. Multilevel and time-series missing value imputation for combined survey and longitudinal context data. Qual Quant (2021). https://doi.org/10.1007/s11135-021-01186-8

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Keywords

  • Multiple imputation
  • Time series imputation
  • Multilevel analysis
  • Institutional trust
  • Cross-national comparative studies
  • Survey methodology