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Missing Data in Multiple Item Scales: A Monte Carlo Analysis of Missing Data Techniques
Abstract
Researchers in many fields use multiple item scales to measure important variables such as attitudes and personality traits, but find that some respondents failed to complete certain items. Past missing data research focuses on missing entire instruments, and is of limited help because there are few variables to help impute missing scores and the variables are often not highly related to each other. Multiple item scales offer the unique opportunity to impute missing values from other correlated items designed to measure the same construct. A Monte Carlo analysis was conducted to compare several missing data techniques. The techniques included listwise deletion, regression imputation, hot-deck imputation, and two forms of mean substitution. Results suggest that regression imputation and substituting the mean response of a person to other items on a scale are very promising approaches. Furthermore, the imputation techniques often outperformed listwise deletion.
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“For the PSWQ, IES-R and DASS-21, individual mean substitution was used up to a maximum of 30% of missing items (Roth et al., 1999). Less than 1% of data was replaced using this approach.”
From Parental Anxiety and Posttraumatic Stress Symptoms in Pediatric Food Allergy. (2021) · cites this paper as Roth et al., 1999
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“Missing values were handled by the mean-person imputation method [24], however, participants were excluded from analyses when more than two items in the QLQ-CIPN16 were missing.”
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“5% of participants had at least 1 missing item in GIDS-PD, which invalidates its total score, but this is below the generally accepted rate for missing values for a psychometric scale (20%).(56,57) As this study was conducted via post with no additional instructions given to participants, the low missingness rates sug…”
ResultRogers, E. R., & King, S. R. (2012) · American Journal of Pharmaceutical Education · doi:10.5688/ajpe768152 · Cited by 38
“As suggested by Roth and colleagues, the individual’s mean response to a particular scale was used to account for item-level missing data.(22) In the final section, students were asked to provide demographic data, including age and gender.”
MethodA threat-appraisal perspective on employees' fears about antisocial workplace behavior.
Sinclair, R. R., Martin, J. E., & Croll, L. W. (2002) · Journal of Occupational Health Psychology · doi:10.1037//1076-8998.7.1.37 · Cited by 38
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“This procedure has been recommended by Roth, Switzer, and Switzer (1999) for managing item-level (rather than variablelevel) missing data where the pattern of missing data is either random or systematic.”
Tomczyk, S., Schomerus, G., Stolzenburg, S., Muehlan, H., & Schmidt, S. (2018) · Social Psychiatry and Psychiatric Epidemiology · doi:10.1007/s00127-018-1537-7 · Cited by 36
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Callous-Unemotional Traits, Harm-Effect Moral Reasoning, and Bullying Among Swedish Children
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“Because we could not know whether additional data were missing at random (MAR) or missing not at random (MNAR), we handled the missing data by applying the expectation maximization (EM), which is available in EQS.”
MethodLynn, M., & Starbuck, M. M. (2014) · Journal of Behavioral and Experimental Economics · doi:10.1016/j.socec.2014.07.005 · Cited by 34
Post-traumatic growth among elderly women with breast cancer compared to breast cancer-free women
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Merenda, F., Trent, J., Rinke, C. R., & Buchanan, M. (2020) · Police Practice and Research · doi:10.1080/15614263.2020.1772784 · Cited by 41
“The MI technique has been shown to create less biased estimates compared to other methods, such as mean value replacement (Allison, 2001; Roth et al., 1999).”
MethodMeasuring market orientation in nonprofit organizations
Modi, P. (2012) · Journal of Strategic Marketing · doi:10.1080/0965254x.2012.689991 · Cited by 34
“Following Roth, Switzer, and Switzer's ( 1999 ) suggestion, the missing data were imputed using the mean value of the person's responses to the other items of the same scale.”
MethodAn Exploration of the Working Alliance in Mental Health Case Management
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An Empirical Investigation of Kaizen Event Effectiveness: Outcomes and Critical Success Factors
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Perceptions of Equity, Balance of Support Exchange, and Mother–Adult Child Relations
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Market orientation in nonprofit organizations: innovativeness, resource scarcity, and performance
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“The missing data were imputed using the mean value of the person's responses to the other items of the same scale (Roth, Switzer, & Switzer, 1999 ).”
MethodParent-Directed Cognitive Behavioral Therapy for Young Anxious Children: A Pilot Study
van der Sluis, C. M., van der Bruggen, C. O., Brechman‐Toussaint, M., Thissen, M., & Bögels, S. M. (2011) · Behavior Therapy · doi:10.1016/j.beth.2011.10.002 · Cited by 35
Whisman, M. A., Richardson, E. D., & Smolen, A. (2011) · Journal of Research in Personality · doi:10.1016/j.jrp.2011.08.009 · Cited by 32
How motivations for tipping vary with occupational differences in descriptive tipping norms
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Gallaty, K., & Zimmer‐Gembeck, M. J. (2007) · Journal of Youth and Adolescence · doi:10.1007/s10964-007-9248-5 · Cited by 31
“Studies of missing data techniques have shown that substituting the mean response of a person to be the most robust approach for handling a modest amount of missing repeated measures data (Roth et al. 1999).”
BackgroundSolberg, P. A., Halvari, H., & Ommundsen, Y. (2013) · Journal of Applied Social Psychology · doi:10.1111/jasp.12088 · Cited by 37
The Effects of Police Satisfaction on Fear of Crime in a Semirural Setting
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“Multiple imputation is advantageous because it creates estimates with less bias and can be used whether data are missing randomly or systematically (Roth et al., 1999).”
BackgroundMethodCognitive behaviour therapy for improving social recovery in psychosis: Cost-effectiveness analysis
Barton, G., Hodgekins, J., Mugford, M., Jones, P. B., Croudace, T. J., & Fowler, D. G. (2009) · Schizophrenia Research · doi:10.1016/j.schres.2009.03.041 · Cited by 31
“, 2002) we used the HDI technique, which has been argued to be superior to other procedures (Roth et al., 1999; Hawthorne and Elliott, 2005).”
MethodEffect on Well-Being from an Online Mindfulness Intervention: “Mindful in May”
Bailey, N. W., Nguyen, J., Bialylew, E., Corin, S. E., Gilbertson, T., Chambers, R., & Fitzgerald, P. B. (2018) · Mindfulness · doi:10.1007/s12671-018-0910-7 · Cited by 40
Lee, M. R., Bartholow, B. D., McCarthy, D. M., Pedersen, S. L., & Sher, K. J. (2014) · Psychology of Addictive Behaviors · doi:10.1037/adb0000015 · Cited by 34
Sauer-Zavala, S. E., Boswell, J. F., Bentley, K. H., Thompson‐Hollands, J., Farchione, T. J., & Barlow, D. H. (2017) · Cognitive Therapy and Research · doi:10.1007/s10608-017-9855-8 · Cited by 31
A 1-Year Follow-Up on Effects of Exercise Programs on Well-Being in Older Adults
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Motivations for tipping: How they differ across more and less frequently tipped services
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Rings, J. A., Genuchi, M. C., Hall, M. D., Angelo, M.-A., & Cornish, J. A. E. (2009) · Training and Education in Professional Psychology · doi:10.1037/a0015054 · Cited by 29
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“Incidentally missing item responses were predicted using the SPSS missing-value analysis based on regression models [46].”
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“Because the presence of missing data in any series has several implications: (I) decrease in the power and accuracy of statistical research methods (Roth et al. 1999), (II) the potential for biased estimates of relationships between two or more variables (Pigott 2001), (III) reduced…”
Metz, S. M., Wyrwich, K. W., Babu, A. N., Kroenke, K., Tierney, W. M., & Wolinsky, F. D. (2007) · Quality of Life Research · doi:10.1007/s11136-007-9225-1 · Cited by 28
“Missing data within each domain were imputed using a hot-deck imputation method [19], using PRELIS 2.”
MethodThe double psychological contracts of temporary agency workers
Morf, M. C., Arnold, A., & Staffelbach, B. (2014) · Employee Relations · doi:10.1108/er-03-2013-0026 · Cited by 27
“Because fewer participants are excluded from the analyses, the chosen procedure might better preserve information than considering a scale score with any scale item missing as missing in total (Roth et al., 1999).”
BackgroundMethodThirukumaran, S., & Sumathi, A. C. (2012) · International Conference on Advanced Computing · doi:10.1109/icoac.2012.6416805 · Cited by 27
A multiple motive perspective on strike propensities
Martin, J. E., & Sinclair, R. R. (2001) · Journal of Organizational Behavior · doi:10.1002/job.93 · Cited by 27
Risk Perception of Musculoskeletal Injury Among Critical Care Nurses
Lee, S., Faucett, J. A., Gillen, M., Krause, N., & Landry, L. G. (2012) · Nursing Research · doi:10.1097/nnr.0b013e31827334d6 · Cited by 26
Datos perdidos y propiedades psicométricas en los tests de personalidad
Cuesta, M., Fonseca‐Pedrero, E., Vallejo, G., & Muñiz, J. (2012) · Anales de Psicología · doi:10.6018/analesps.29.1.137901 · Cited by 26
Schomerus, G., Muehlan, H., Auer, C., Horsfield, P., Tomczyk, S., Freitag, S., Evans-Lacko, S., Schmidt, S., & Stolzenburg, S. (2019) · Psychiatry Research · doi:10.1016/j.psychres.2019.01.054 · Cited by 24
“When computing total scores for the SELF-I, PHQ-9 and PHQ-15, we imputed missing values using the individual mean participant response of the respective scale if no more than 25% of values were missing (Downey and King, 1998; Roth et al., 1999).”
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“Although some comparative Monte Carlo studies have been carried out to compare methods, these studies generally: (1) concern types of data ( Roth, Switzer & Switzer, 1999 ) or methods (Bello, 1993a, 1995; Liu et al., 1997) that are not relevant to morphometric studies; (2) have been aimed at evaluating the effects of…”
ResultThe Tipping Behavior and Motives of US Travelers Abroad: Affected by Host Nations’ Tipping Norms?
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“In constructing these indices, any missing values were replaced with the mean of the other items as advocated by Roth, Switzer, and Switzer (1999).”
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“To address missing values, when less than 20 % of items in a scale were missing, average of non-missing values on that scale was substituted [26–28].”
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Police satisfaction and disorder: results from a survey of a semi-rural community
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Cross‐level effects of support climate: Main and moderating roles
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“In practice, however, missing data can result from any combination of these three causes (Graham, 2009; Roth et al., 1999).”
BackgroundA study of error reporting by nurses: the significant impact of nursing team dynamics
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“Consistent with other studies, missing item values for a scale were replaced using imputation by individual means of non-missing items for participants if there were no more than 30% such missing item responses for a given scale (Roth et al., 1999).”
MethodParental Anxiety and Posttraumatic Stress Symptoms in Pediatric Food Allergy.
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“intercorrelated items designed to measure the same construct (Roth et al., 1999).”
BackgroundEstimating the reliability coefficient of tests in presence of missing values
Cuesta, M., & Fonseca‐Pedrero, E. (2014) · Psicothema · doi:10.7334/psicothema2014.98 · Cited by 18
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“Roth et al. (1999) referred to this technique and person-mean MDR as ‘‘very promising approaches’’ (1999: 211) and reported Monte Carlo evidence in support of this characterization.”
MethodInfluentialSimons, R. L., Ong, M. L., Lei, M., Beach, S. R. H., Zhang, Y., Philibert, R. A., & Mielke, M. M. (2024) · Alzheimer s & Dementia · doi:10.1002/alz.13751 · Cited by 17
Hart, P. L., & Grindel, C. G. (2010) · Journal of Nursing and Healthcare of Chronic Illness · doi:10.1111/j.1752-9824.2010.01062.x · Cited by 17
Littlewood, K., Swanke, J. R., Strozier, A., & Kondrat, D. C. (2012) · PubMed · Cited by 17
Examining the Validity of the Rush Protocol to Screen for Religious/Spiritual Struggle
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Xiong, Z. B., Rettig, K. D., & Tuicomepee, A. (2008) · The Journal of Psychology · doi:10.3200/jrlp.142.4.337-356 · Cited by 17
The impact of childhood sexual abuse on sleep in adulthood
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Alzahrani, H. A., Mackey, M., Stamatakis, E., & Shirley, D. (2021) · PLoS ONE · doi:10.1371/journal.pone.0256459 · Cited by 15
“Missing data were replaced with the mean value for each item [62].”
MethodKiyang, L.-N., Labrecque, M., Doualla‐Bell, F., Turcotte, S., Farley, C., Bas, M. C., Blais, J., & Légaré, F. (2015) · BMC Research Notes · doi:10.1186/s13104-015-1608-8 · Cited by 16
“We imputed missing values (Monte Carlo method) [16] for all respondents who answered two out of three items used in assessing each variable.”
MethodClassifying Revenue Management: A Taxonomy to Assess Business Practice*
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“Although item response theory software is designed to handle missing data, the missing data (<2%) within each disease-specific domain were imputed via a hot-deck imputation method [18], using PRELIS 2.”
MethodMultilevel analysis of achievement in mathematics of Malaysian and Singaporean students
Ghagar, M. N. A., Othman, R. B., & Mohammadpour, E. (2011) · Cited by 16
Beogo, I., Rojas, B. M., Gagnon, M., & Liu, C. (2016) · Nurse Education Today · doi:10.1016/j.nedt.2016.08.007 · Cited by 16
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Competitive aggressiveness, community banking and performance
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Krauss, S. W., Zust, J., Frankfurt, S. B., Kumparatana, P., Riviere, L. A., Hocut, J., Sowden, W. J., & Adler, A. B. (2020) · Journal of Traumatic Stress · doi:10.1002/jts.22635 · Cited by 17
Development of the Resident Wellness Scale for Measuring Resident Wellness
Stansfield, R. B., Giang, D., & Markova, T. (2019) · Journal of patient-centered research and reviews · doi:10.17294/2330-0698.1653 · Cited by 14
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“Furthermore, listwise deletion of observations for which we did not receive any data on multi-item scales to calculate the mean (Roth et al., 1999) or which had missing values on the observed variables (e.g., gender) resulted in a final sample of 1,355 volunteers (23% of the contacted volunteers)…”
BackgroundDistributive Justice for Volunteers
Hurst, C., Scherer, L. L., & Allen, J. A. (2016) · Nonprofit Management and Leadership · doi:10.1002/nml.21251 · Cited by 21
Hahm, S., Muehlan, H., Stolzenburg, S., Tomczyk, S., Schmidt, S., & Schomerus, G. (2019) · Stigma and Health · doi:10.1037/sah0000184 · Cited by 13
Methodological approaches for imputing missing data into monthly flows series
Bleidorn, M. T., Pinto, W. D. P., Schmidt, I. M., Mendonça, A. S. F., & dos Reis, J. A. T. (2022) · Ambiente e Agua - An Interdisciplinary Journal of Applied Science · doi:10.4136/ambi-agua.2795 · Cited by 13
“As discussed by Roth et al. (1999) and Pigott (2001), the existence of missing values in time series generally decreases the capacity and precision of statistical analysis approaches and contributes to biased estimates of the relationship between variables, which may cause inaccurate assumptions in…”
BackgroundEconomic Motivations and Moral Controls Regulating Discrimination Against Black and Hispanic Diners
Brewster, Z. W., Brauer, J. R., & Lynn, M. (2015) · Sociological Quarterly · doi:10.1111/tsq.12093 · Cited by 13
“…imputation at the item level preserves a great deal of information while yielding efficient and unbiased results when a multi-item scale is unidimensional and has a relatively high reliability (e.g., alpha > .50, cf. Roth, Switzer, and Switzer 1999:229; Jeličić, Phelps, and Lerner 2010:823).”
BackgroundCan Experiential–Didactic Training Improve Clinical STD Practices?
Dreisbach, S., Devine, S., Fitch, J., Anderson, T. S., Lee, T., RIETMEIJER, C. A. M., & Corbett, K. K. (2011) · Sexually Transmitted Diseases · doi:10.1097/olq.0b013e3182045306 · Cited by 13
Examining workgroup diversity effects: does playing by the (group-retention) rules help or hinder?
Stanley, D., Allen, N. J., Williams, H. M., & Ross, S. J. (2011) · Behavior Research Methods · doi:10.3758/s13428-010-0053-9 · Cited by 15
“The mean absolute error values in these graphs were calculated using Eq. 1 below (K represents the number of replications)—a modified version of the absolute error approach used by Roth, Switzer, and Switzer (1999) .”
MethodThe meaning and relevance of internal market orientation in nonprofit organisations
Modi, P., & Sahi, G. K. (2017) · Service Industries Journal · doi:10.1080/02642069.2017.1376660 · Cited by 13
Rogers, E. R., & King, S. R. (2013) · Journal of the American Pharmacists Association · doi:10.1331/japha.2013.11231 · Cited by 12
Psychosocial Predictors of Change in Depressive Symptoms Following Gastric Banding Surgery
Preiss, K., Clarke, D. M., O’Brien, P. E., Garcia, X. D. L. P., Hindle, A., & Brennan, L. (2018) · Obesity Surgery · doi:10.1007/s11695-017-3055-1 · Cited by 12
Serrani, D. (2011) · Revista Española de Geriatría y Gerontología · doi:10.1016/j.regg.2011.09.005 · Cited by 12
Rosenthal, S. (2017) · The International Encyclopedia of Communication Research Methods · doi:10.1002/9781118901731.iecrm0058 · Cited by 12
Bailey, N. W., Comte, W., Chambers, R., Bartlett, L., Connaughton, S., & Hassed, C. S. (2023) · Mindfulness · doi:10.1007/s12671-023-02168-7 · Cited by 13
“The case mean substitution method was applied for imputing missing scores for individual items within a scale at the pre-program timepoint, which has been demonstrated to improve statistical power in a study while not biasing the values of the measures (Bono et al., 2007; Roth et al., 1999).”
MethodJacobson, C. M., Hill, R. M., Pettit, J. W., & Miranda, R. (2014) · Journal of Psychopathology and Behavioral Assessment · doi:10.1007/s10862-014-9463-9 · Cited by 11
“Where 80 % of data were present for a given scale, individual-level mean imputation was used to calculate prorated scales (Roth et al. 1999), which resulted in no missing data at the variable level.”
MethodSelf-assessment of Foot Health
Trevethan, R. (2009) · Journal of the American Podiatric Medical Association · doi:10.7547/0990460 · Cited by 11
Metadata
- Authors
- Roth, P. L., Switzer, F. S., & Switzer, D. M.
- Affiliations
- Clemson University (US)
- Venue
- Organizational Research Methods
- Publisher
- SAGE Publications
- Published
- 1999-07
- Volume
- 2
- Issue
- 3
- Pages
- 211-232
- ISSN
- 1094-4281 (ISSN-L)
- 1552-7425
- OpenAlex
- W2122169890
- Cited by
- 344
- References
- 39
- Citations by year
- 2026: 5 · 2025: 7 · 2024: 11 · 2023: 8 · 2022: 17 · 2021: 14 · 2020: 16 · 2019: 20 · 2018: 28 · 2017: 17 · 2016: 15 · 2015: 19 · 2014: 19 · 2013: 21 · 2012: 26
- FWCI
- 2.99
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Organizational Research Methods (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Social Sciences › Sociology and Political Science › Survey Methodology and Nonresponse
- Keywords
- missing data, regression imputation, hot deck imputation, mean substitution, listwise deletion, imputation accuracy, attitudes, personality traits
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