Available-Case Analysis: Missing Data Explained

Missing data represent one of the most pervasive methodological challenges across empirical research, threatening statistical power, sample representativeness, and inferential validity. In quantitative disciplines ranging from psychometrics to epidemiology, researchers routinely confront incomplete datasets and must select principled approaches to handle missing values. Available-case analysis—commonly referred to in bivariate contexts as pairwise deletion—constitutes a foundational ad hoc technique designed to salvage as much observational information as possible without discarding entire participant records.

Available-Case Analysis

1. Concise Definition

Available-case analysis is a statistical missing-data handling procedure in which each specific parameter, summary statistic, or bivariate association is estimated using all observed observations that contain complete data for the exact variables involved in that computation. Rather than eliminating an entire observational unit when a single variable is missing, this method dynamically adjusts the analytical sample size on an estimate-by-estimate basis to preserve all recorded measurements.

In bivariate and multivariate statistical modeling, available-case analysis is most widely recognized as pairwise deletion. When constructing a correlation or covariance matrix under pairwise deletion, the correlation between any two variables, $X_j$ and $X_k$, is calculated using only those participants who provided valid responses for both $X_j$ and $X_k$, regardless of whether those participants have missing values on other variables in the dataset. Consequently, different elements of the summary matrix are derived from different subsamples and distinct sample sizes.

While available-case analysis retains substantially more raw data than complete-case analysis (listwise deletion), it introduces complex methodological vulnerabilities. Because each parameter can be based on a distinct subset of the sample, the resulting correlation or covariance matrices may fail to be mathematically consistent or positive semi-definite, complicating subsequent multivariate procedures such as multiple linear regression, exploratory factor analysis, and structural equation modeling.

2. Etymology & Linguistic Origin

The term available-case analysis is an English descriptive compound combining the adjective “available” (derived from the Middle English availen, rooted in the Old French valoir, meaning “to be worth” or “to be of use,” originating from the Latin valere, “to be strong or worthy”) and the noun “case” (from the Latin casus, meaning “a fall, chance, occurrence, or event”). Historically, statistical methodology used the term “case” to refer to an individual subject, participant, or observational record within a data matrix.

The synonym pairwise deletion entered the lexicon of computational statistics in the mid-twentieth century with the advent of automated statistical computing packages such as the Statistical Package for the Social Sciences (SPSS) and the Biomedical Computer Programs (BMDP). The modifier “pairwise” denotes that decisions regarding inclusion or exclusion are negotiated strictly across pairs of variables, contrasting directly with “listwise” operations, which purge records across the entire list of investigated attributes.

During the formalization of missing data theory in the late 1970s and 1980s, mathematical statisticians systematically adopted the phrase “available-case analysis” to encompass both univariate parameter estimations (such as calculating variable means from all available instances) and bivariate calculations, establishing it as a standard taxonomic category alongside complete-case analysis and imputation techniques.

3. Pronunciation & Grammatical Form

The term is pronounced phonetically in International Phonetic Alphabet (IPA) transcription as /əˈveɪ.lə.bəl keɪs əˈnæl.ə.sɪs/. Grammatically, it functions as a compound noun phrase. When modifying another noun, it frequently adopts a hyphenated adjectival form, as in “available-case estimators” or “available-case sample size.”

Its primary operational synonym, pairwise deletion (/ˈpɛər.waɪz dɪˈliː.ʃən/), functions similarly as a noun phrase denoting the explicit computational mechanism of dropping non-overlapping pairs. In scholarly discourse, researchers frequently alternate between “analyzing available cases,” “relying on an available-case framework,” and “employing pairwise deletion algorithms.”

4. Detailed Conceptual Explanation

To grasp the conceptual architecture of available-case analysis, one must contrast it with complete-case analysis, widely known as listwise deletion. In listwise deletion, any observational row containing even a single missing value across any variable included in the planned analysis is entirely purged. If a study collects fifty variables and a respondent omits only the fiftieth item, listwise deletion discards the entirety of that participant’s forty-nine valid answers. Available-case analysis was formulated specifically to mitigate this profound loss of statistical power and observational investment.

Under an available-case framework, univariate parameters such as the sample mean $\bar{X}_j$ and variance $s^2_j$ of variable $X_j$ are calculated using the total number of individuals who provided data for $X_j$, denoted as $N_j$. If variable $X_1$ has 500 valid responses out of a total cohort of 600, its mean is calculated using $N_1 = 500$. If variable $X_2$ has 580 valid responses, its mean is calculated using $N_2 = 580$. When evaluating bivariate associations, such as the Pearson product-moment correlation coefficient $r_{jk}$ between $X_j$ and $X_k$, the algorithm restricts calculations strictly to the intersecting subset of cases where both $X_j$ and $X_k$ are non-missing, denoted as $N_{jk}$.

Although this dynamic sample resizing maximizes sample utilization, it creates severe structural anomalies in multivariate matrices. In a standard correlation matrix derived from complete data, every correlation coefficient shares a common sample size ($N$). Under pairwise deletion, every off-diagonal element $r_{jk}$ in the correlation matrix may reflect a distinct sample size ($N_{jk}$), and the diagonal elements (variances) may reflect yet another set of sample sizes ($N_j$). Consequently, the relationships among variables are calculated across slightly differing subpopulations.

This inconsistency can distort the geometric properties of variance-covariance matrices. In mathematical terms, a valid correlation or covariance matrix must be positive semi-definite, meaning that all of its eigenvalues are greater than or equal to zero, and its determinant is non-negative. Because pairwise deletion derives correlations from disparate subgroups, it can produce mathematically impossible matrices where eigenvalues become negative or the determinant falls below zero. Such “non-positive definite” matrices cannot be inverted, precipitating mathematical errors in structural equation models, multiple regression equations, and factor analyses.

Furthermore, available-case analysis complicates the determination of standard errors and degrees of freedom. In ordinary hypothesis testing, calculating the standard error of a regression slope requires a definitive sample size ($N$). In an available-case covariance matrix where $N_{12} = 450$, $N_{23} = 380$, and $N_{13} = 510$, there is no single, unambiguous sample size to input into multivariate standard error formulas. Statistical programs historically resolved this ambiguity through ad hoc conventions, such as using the minimum sample size, the maximum sample size, the arithmetic mean, or the harmonic mean of the pairwise counts—each of which distorts Type I error rates and statistical inference.

5. Historical Development

The handling of missing data has challenged statisticians since the initial development of applied multivariate analysis in the early twentieth century. In agricultural experiments, early pioneers such as Frank Yates (1933) and Ronald A. Fisher devised specialized algebraic adjustments to recover missing plot values in balanced experimental layouts. However, these techniques were primarily deterministic balancing corrections suited for agricultural designs rather than general solutions for observational datasets.

During the expansion of mainframe computational power in the 1960s and 1970s, social scientists began managing large-scale national surveys containing ubiquitous item non-response. To automate data processing, statistical software packages implemented default missing-data routines. Listwise deletion was frequently set as the conservative default, but pairwise deletion was offered as a high-powered alternative. Software documentation emphasized pairwise deletion as an efficient way to “waste no data,” leading to its widespread adoption across behavioral and organizational research throughout the 1970s and 1980s.

A watershed moment in the formalization of missing data methodology occurred in 1976 when Donald B. Rubin published his seminal paper, “Inference and Missing Data,” in Biometrika. Rubin established the canonical taxonomy of missingness mechanisms: Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR). Following Rubin’s theoretical breakthrough, Roderick J. A. Little and Donald B. Rubin published their definitive 1987 monograph, Statistical Analysis with Missing Data. Their work exposed the mathematical hazards of available-case analysis, demonstrating that it yields consistent and unbiased estimates only under the rigorous assumption of MCAR, and that even under MCAR, its standard errors are unstable and its matrices often mathematically invalid.

By the late 1990s and early 2000s, the development of modern algorithmic solutions—most notably multiple imputation (MI) and full information maximum likelihood (FIML)—drastically diminished the academic justification for pairwise deletion. Prominent methodological task forces, such as the American Psychological Association’s Task Force on Statistical Inference (Wilkinson et al., 1999), formally advised against available-case analysis, urging researchers to transition to likelihood-based or multiple imputation frameworks.

6. Theoretical Foundations

The statistical viability of available-case analysis depends directly on Donald Rubin’s foundational taxonomy of missing-data mechanisms. Let $Y = (Y_{\text{obs}}, Y_{\text{mis}})$ represent a complete data matrix partitioned into observed and missing components, and let $R$ denote a corresponding indicator matrix where $R_{ij} = 1$ if variable $j$ for subject $i$ is observed, and $R_{ij} = 0$ if it is missing.

The three distinct mechanisms defined by Rubin include:

• Missing Completely at Random (MCAR): The probability of missingness is entirely independent of both observed and unobserved data, expressed mathematically as $P(R mid Y_{\text{obs}}, Y_{\text{mis}}, \phi) = P(R mid \phi)$, where $phi$ represents the parameters governing the missingness mechanism. Under MCAR, the observed data points represent a true simple random subsample of the original population.
• Missing at Random (MAR): The probability of missingness depends systematically on observed data values but is conditionally independent of the missing values themselves, expressed as $P(R mid Y_{\text{obs}}, Y_{\text{mis}}, \phi) = P(R mid Y_{\text{obs}}, \phi)$.
• Missing Not at Random (MNAR): The probability of missingness depends directly on the unobserved values themselves, even after conditioning on all available observed data, expressed as $P(R mid Y_{\text{obs}}, Y_{\text{mis}}, \phi)$.

For available-case analysis to produce unbiased estimates of population means, variances, and bivariate correlations, the data must satisfy the stringent assumption of MCAR. If the missingness mechanism is MAR—where, for instance, older participants are less likely to report income, but age is fully measured—available-case correlation estimates between income and other attributes become systematically biased. Because the pairwise algorithm computes each correlation across a distinct subgroup without adjusting for the observed covariates driving the non-response, the resulting sample moments deviate systematically from the true population parameters.

Even when the MCAR assumption is satisfied, available-case analysis lacks an underlying joint probability distribution. In likelihood-based estimation (such as FIML), a single unified likelihood function describes the entire dataset based on the observed data distribution. In contrast, available-case analysis constructs a synthetic correlation or covariance matrix pieced together from separate bivariate estimations. Consequently, it violates the likelihood principle, providing no unified probabilistic framework for computing accurate standard errors, confidence intervals, or omnibus model fit statistics.

7. Key Components, Types & Dimensions

The operational framework of available-case analysis can be deconstructed into several specific structural components, dimensions, and operational variants:

• Univariate Available-Case Estimation: The computation of central tendency (mean, median) and dispersion (variance, standard deviation) for each variable independently, using all available valid responses ($N_j$) for that single column.
• Bivariate Pairwise Deletion: The calculation of bivariate measures of association—such as Pearson’s $r$, Spearman’s $rho$, Kendall’s $tau$, or bivariate linear regressions—using cases that possess valid data on both variables ($N_{jk}$).
• Pairwise-Constructed Correlation/Covariance Matrices: The compilation of full multivariate association matrices by assembling individually computed pairwise covariances or correlations. The resulting matrix has varying effective sample sizes across its non-diagonal elements.
• Sample Size Disparity Ratio: The degree of divergence between the maximum and minimum pairwise sample sizes ($N_{\text{\max}} / N_{\text{\min}}$) within a single matrix. Higher disparity ratios dramatically escalate the risk of non-positive definite matrices and severe standard error distortion.
• Matrix Conditioning and Indefiniteness: A structural dimension reflecting the mathematical validity of the resulting matrix. Matrices may be well-conditioned (positive definite, all positive eigenvalues) or ill-conditioned/indefinite (containing zero or negative eigenvalues, leading to computational collapse in matrix inversion).
• Ad Hoc Degrees of Freedom Adjustments: The computational conventions employed by software programs to conduct inferential tests on pairwise matrices, including selecting the minimum pairwise $N$, the mean pairwise $N$, or pairwise-specific degrees of freedom ($N_{jk} – 2$).

8. Examples & Illustrative Cases

To demonstrate the mechanics and failure modes of available-case analysis, consider a clinical psychology study investigating burnout among healthcare professionals. The researchers measure three continuous variables across an initial sample of 100 participants: Emotional Exhaustion ($X_1$), Workplace Stress ($X_2$), and Sleep Quality ($X_3$). Due to survey fatigue and time constraints, missing data occur across the measures.

Suppose all 100 participants complete the Emotional Exhaustion scale ($N_1 = 100$). However, 20 participants skip the Workplace Stress battery, leaving 80 responses ($N_2 = 80$). Furthermore, 25 participants skip the Sleep Quality inventory, leaving 75 responses ($N_3 = 75$). Among those who skipped questions, 15 participants missed both Workplace Stress and Sleep Quality.

Under a complete-case (listwise deletion) approach, any participant with even one missing value is excluded. Because 20 participants missed $X_2$, 25 missed $X_3$, and 15 missed both, a total of 30 participants have incomplete records ($20 + 25 – 15 = 30$). Listwise deletion discards all 30 individuals, reducing the analytical cohort from 100 to 70 cases, sacrificing 30% of the sample power.

Under an available-case (pairwise deletion) approach, the researchers construct their correlation matrix using every available pair:

• The correlation between Emotional Exhaustion ($X_1$) and Workplace Stress ($X_2$) is computed using all participants who answered both: $N_{12} = 80$.
• The correlation between Emotional Exhaustion ($X_1$) and Sleep Quality ($X_3$) is computed using all participants who answered both: $N_{13} = 75$.
• The correlation between Workplace Stress ($X_2$) and Sleep Quality ($X_3$) is computed using participants who completed both scales: $N_{23} = 70$.

While this pairwise procedure retains more data than listwise deletion, consider what occurs if the missingness on Sleep Quality is driven by severe stress (an MAR mechanism). Participants suffering the highest stress and poorest sleep may have omitted the Sleep Quality measure. In the pairwise calculation of $r_{12}$, those highly stressed participants are fully included, producing an accurate correlation between exhaustion and stress. However, in the calculation of $r_{23}$, those stressed individuals are disproportionately absent. The correlation matrix is now synthesized from fundamentally non-equivalent subsamples. If the researchers input this composite matrix into a multiple regression model to predict sleep quality from exhaustion and stress, the resulting standardized regression coefficients ($eta$) can exceed the absolute boundary of $1.0$ or produce impossible negative variance estimates (Heywood cases).

9. Measurement & Assessment

When working with incomplete data, researchers must rigorously assess the extent, patterning, and statistical mechanisms of missingness prior to adopting or evaluating an available-case design. Methodological assessment proceeds through several diagnostic stages.

First, analysts construct missing data patterns and frequency tables. This involves calculating the percentage of missing values per variable, the percentage of incomplete records per participant, and mapping the unique missingness configurations across the dataset. Software packages generate missing-pattern matrices indicating which combinations of variables are most frequently omitted.

Second, researchers evaluate whether the data conform to the MCAR assumption required for pairwise estimates to remain unbiased. The most common statistical evaluation is Roderick Little’s omnibus MCAR test (Little’s MCAR test). Little’s test evaluates mean differences across distinct missing-value patterns using a chi-square metric:

$$d^2 = \sum_{k=1}^K n_k (\bar{y}_{\text{obs}, k} – \hat{\mu}_{\text{obs}, k})^T \hat{\Sigma}_{\text{obs}, k}^{-1} (\bar{y}_{\text{obs}, k} – \hat{\mu}_{\text{obs}, k})$$

A statistically significant chi-square test ($p < .05$) indicates that the missing data depart from MCAR, demonstrating that the observed values systematically correlate with missingness patterns. Under such conditions, available-case analysis is empirically invalidated and will yield biased parameter estimates.

Third, if an available-case correlation or covariance matrix is computed, researchers must evaluate its numerical stability. Diagnostic assessment involves calculating the matrix determinant and conducting an eigenvalue decomposition. If any eigenvalue is negative or zero, or if the determinant is negative, the matrix is indefinite. Analysts must also calculate the condition number of the matrix (the ratio of the largest eigenvalue to the smallest eigenvalue). An excessively large condition number signifies severe multicollinearity and numerical instability caused by pairwise sampling disparities, alerting the researcher that linear models based on this matrix will produce erroneous results.

10. Applications & Practical Significance

Historically, available-case analysis found widespread application across virtually all empirical disciplines that collect survey or observational data, including personality psychology, sociology, educational testing, organizational behavior, and public health. In preliminary exploratory research, pairwise deletion was widely used to inspect large bivariate correlation matrices during scale development and exploratory factor analyses.

In modern research environments, the direct practical application of available-case analysis has narrowed considerably due to methodological advances. However, it remains relevant in several practical contexts:

• Exploratory Data Screening: Analysts frequently compute pairwise correlation matrices during rapid exploratory data inspection to evaluate preliminary zero-order associations without spending the substantial computational time required to build complex imputation models.
• Planned Missing Data Designs: In large-scale educational testing frameworks (such as PISA or NAEP) and split-questionnaire survey designs, items are deliberately administered to randomized subsets of respondents to minimize participant burden. Because items are assigned missing values strictly at random by experimental design, the data satisfy MCAR by definition. While modern testing programs primarily analyze these designs via item response theory and FIML, pairwise summaries provide quick baseline benchmarks.
• Legacy Data Re-Analysis and Meta-Analysis: Meta-analysts routinely synthesize historical correlation matrices published in older empirical literature where authors relied on pairwise deletion. Understanding the biases and limitations of available-case statistics is critical for evaluating the validity of meta-analytic structural equation models (MASEM) based on older primary studies.
• High-Dimensional Genomic and Sensor Screening: In preliminary screening of massive bioinformatic datasets or streaming wearable-sensor outputs where missingness occurs haphazardly across millions of data points, available-case calculations can serve as computationally lightweight screening filters prior to executing intensive probabilistic pipelines.

11. Research & Empirical Evidence

Methodologists have extensively evaluated the performance of available-case analysis using Monte Carlo simulation studies, comparing its efficiency, bias, and stability against complete-case analysis, mean imputation, multiple imputation, and full information maximum likelihood.

Early simulation research conducted by Roderick Little (1988, 1992) demonstrated that although available-case analysis generally exhibits higher statistical efficiency (smaller variance of estimators) than complete-case analysis when correlations among variables are low, this advantage rapidly dissipates when correlations are moderate to high. In the presence of substantial intercorrelations, pairwise covariance matrices often yield regression slope estimates that are substantially more variable and unstable than those produced by listwise deletion, even under pure MCAR conditions.

In a seminal simulation study, Craig K. Enders and Deborah L. Bandalos (2001) systematically evaluated missing data handling methods across structural equation models with varying sample sizes and missing data mechanisms. Their findings revealed that pairwise deletion produced substantial parameter bias under MAR conditions and demonstrated severe convergence failures due to non-positive definite covariance matrices. In contrast, Full Information Maximum Likelihood (FIML) consistently delivered unbiased parameter estimates and accurate standard errors across all evaluated MAR conditions.

Further methodological work by John W. Graham (2009) and Joseph L. Schafer (1997) corroborated these risks, showing that under pairwise deletion, the standard errors calculated by standard statistical software packages are profoundly compromised. Software algorithms routinely default to setting $N$ equal to the total number of individuals who completed any variable, or to the mean pairwise $N$. Graham demonstrated that this computational compromise inflates Type I error rates in multiple regression, producing false-positive statistical significance for coefficients that are actually null in the population.

12. Cultural & Cross-Cultural Considerations

Cross-cultural, cross-national, and multi-linguistic research settings present unique challenges for missing data handling, amplifying the systemic risks of available-case analysis. In global comparative initiatives—such as the World Values Survey, the International Social Survey Programme (ISSP), and cross-national epidemiological assessments—missing data rarely occur completely at random.

Cultural norms, taboos, and systemic sociopolitical factors heavily influence item non-response. For example, survey items addressing personal household income, religious devotion, political alignment, sexual behavior, or mental health symptoms elicit vastly different non-response rates across differing cultural contexts. In conservative or politically restrictive nations, items regarding political dissent or non-traditional social attitudes experience elevated refusal rates, whereas identical questions yield near-complete compliance in liberal democracies.

When cross-cultural researchers deploy available-case analysis across diverse national cohorts, the effective sample composition shifts across cultural contexts. For sensitive variables, the available cases in one nation may represent a highly atypical, privileged, or ideologically unrepresentative subgroup, whereas the available cases in another nation represent the general population. Computing pairwise correlations between such variables and demographic markers creates severe cross-national equivalence bias. The resulting cultural differences in correlation coefficients often reflect differential non-response mechanisms rather than substantive psychological or cultural variations.

Consequently, international methodological bodies strongly mandate against available-case analysis in comparative research, advocating instead for culturally informed Multiple Imputation by Chained Equations (MICE) or multi-group structural equation modeling that explicitly incorporates cultural covariates to satisfy Missing at Random (MAR) assumptions.

13. Criticisms, Debates & Limitations

The academic consensus within modern quantitative methodology is overwhelmingly critical of available-case analysis for primary inferential testing. The central criticisms, theoretical debates, and mathematical limitations of this approach include:

• Vulnerability to MAR and MNAR Bias: Pairwise deletion requires the unrealistic assumption of Missing Completely at Random (MCAR). Because empirical missingness in real-world human research almost invariably correlates with observed covariates (MAR) or the unobserved variables themselves (MNAR), available-case parameter estimates are systematically biased.
• Mathematical Indefiniteness of Covariance Matrices: Because every cell in a pairwise matrix is computed from a distinct subset of individuals, the collective matrix frequently violates the fundamental mathematical axioms of symmetric positive semi-definite matrices. This leads to negative eigenvalues, negative determinants, impossible correlations ($|r| > 1.0$), and fatal computational errors during matrix inversion.
• Ambiguity of Degrees of Freedom and Standard Errors: There is no coherent, single sample size ($N$) underlying a pairwise matrix. Software packages use arbitrary heuristics (e.g., minimum pairwise $N$, mean $N$, or listwise $N$) to calculate standard errors and $p$-values, resulting in distorted test statistics, inaccurate confidence intervals, and inflated Type I error rates.
• Impossibility of Global Model Fit Assessment: Multivariate statistical frameworks such as confirmatory factor analysis and structural equation modeling rely on chi-square fit statistics and incremental fit indices (CFI, TLI, RMSEA) that require a single global log-likelihood and a fixed sample size. Pairwise deletion cannot generate valid global fit statistics, preventing researchers from assessing overall model adequacy.
• Suppression and Collinearity Artefacts: Discrepancies between pairwise subsets can artificially create or mask collinearity among predictors in multiple regression models, occasionally generating extreme mathematical artifacts such as negative residual variances (Heywood cases) and sign reversals in regression weights.

14. Related Terms & Distinctions

To contextualize available-case analysis within modern quantitative methodology, it is essential to distinguish it from alternative missing data strategies:

• Listwise Deletion (Complete-Case Analysis): An exclusion strategy that discards any observational row containing missing data on any variable in the model. In contrast to available-case analysis, listwise deletion guarantees a single, uniform sample size ($N$) and ensures positive semi-definite matrices, but at the cost of substantial statistical power loss and severe bias when data are not MCAR.
• Mean Substitution (Mean Imputation): An ad hoc procedure that replaces missing values with the arithmetic mean of the observed values for that variable. While mean substitution preserves the original sample size, it artificially deflates sample variance, distorts covariance structures, and severely attenuates correlation coefficients, rendering it statistically inferior to available-case analysis.
• Full Information Maximum Likelihood (FIML): A modern model-based estimation method that calculates the log-likelihood for each participant using all variables observed for that specific individual, directly maximizing the joint sample likelihood. Unlike available-case analysis, FIML operates under the broader, more realistic Missing at Random (MAR) assumption, preserves mathematical validity, and generates accurate standard errors.
• Multiple Imputation (MI): A flexible simulation-based methodology that replaces each missing value with a set of $m$ plausible values generated from an imputation model, creating $m$ complete datasets. Each dataset is analyzed independently, and results are pooled using Rubin’s rules. MI handles MAR mechanisms, preserves matrix positive-definiteness, and correctly accounts for missing-data uncertainty.
• Pairwise Deletion: The specific operational implementation of available-case analysis applied to bivariate association metrics (e.g., correlations, covariances). In scholarly literature, “pairwise deletion” and “available-case analysis” are frequently used interchangeably when discussing correlation matrices.

15. Summary & Key Takeaways

Available-case analysis represents an intuitive, historically prominent approach to missing data handling that utilizes all valid observations for each specific estimation rather than discarding entire participant records. While it succeeds in retaining more raw observational data than complete-case analysis, its mathematical and statistical drawbacks are severe.

Because available-case analysis calculates separate statistics across varying, non-identical subsamples, it frequently produces mathematically inconsistent, non-positive definite correlation and covariance matrices. It yields unbiased parameter estimates only under the strict, rarely met assumption that data are Missing Completely at Random (MCAR). Furthermore, it provides no principled mechanism for calculating accurate degrees of freedom, standard errors, or global goodness-of-fit indices in multivariate models.

In contemporary academic research, methodologists consider available-case analysis largely obsolete for formal hypothesis testing and structural modeling. Investigators are strongly advised to adopt state-of-the-art principled methods—specifically Full Information Maximum Likelihood (FIML) or Multiple Imputation (MI)—which provide mathematically sound, unbiased inference under the substantially more plausible assumption of Missing at Random (MAR).

In conclusion, while available-case analysis remains an informative concept in the history of computational statistics and a convenient tool for quick exploratory screening, its structural liabilities make it unsuitable for rigorous multivariate research. Modern empirical science demands robust methodologies that simultaneously respect data integrity, accommodate complex missingness mechanisms, and preserve the fundamental mathematical properties of statistical estimators.

References

• Enders, C. K., & Bandalos, D. L. (2001). The relative performance of full information maximum likelihood estimation for missing data in structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 8(3), 430–457. https://doi.org/10.1207/S15328007SEM0803_5
• Graham, J. W. (2009). Missing data analysis: Making it work in the real world. Annual Review of Psychology, 60, 549–576. https://doi.org/10.1146/annurev.psych.58.110405.085530
• Little, R. J. A. (1988). A test of missing completely at random for multivariate data with missing values. Journal of the American Statistical Association, 83(404), 1198–1202. https://doi.org/10.1080/01621459.1988.10478722
• Little, R. J. A., & Rubin, D. B. (2019). Statistical analysis with missing data (3rd ed.). John Wiley & Sons. https://doi.org/10.1002/9781119482260
• Rubin, D. B. (1976). Inference and missing data. Biometrika, 63(3), 581–592. https://doi.org/10.1093/biomet/63.3.581
• Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7(2), 147–177. https://doi.org/10.1037/1082-989X.7.2.147