Choosing Statistical and Econometric Methods

A guide to data types and research questions: a practical guide to analytical methods and techniques

By bipul paul

Classification of statistical and econometric methods according to their analytical objectives and data requirements. The choice of procedure is indicated only after the research question has been formulated, the outcome variable identified, the data structure examined and the method's assumptions scrutinized.

1. Start with the Data and Research Design

A suitable method must match both the measurement scale of the variables and the structure of the observations.

Nominal: unordered categories, for example, regions or occupations.

Binary: two categories, for example, success or failure.

Ordinal: ordered categories, for example, low, medium, high.

Continuous: measured values, for example, income, heights, costs, or outputs.

Count: number of hits, for example, visits or incidents.

Limited: outcomes are affected by censoring, truncation, an excess of zeros, or selection.

Multivariate: multiple variables are analyzed.

Hierarchical: observations nested in groups, for example, workers in firms.

Spatial: locations or neighbors.

Cross-sectional: the number of units observed at a point in time.

Time-series: time-related observations of variables.

Panel: the same units are observed at different points in time.

 

2. Describe and Explore the Data

Exploratory analysis should come before formal testing or modelling. It helps identify data errors, unusual values, distributional patterns, and possible relationships.

Categorical variables: frequencies, percentages, mode, cross-tabulations, and bar charts.

Numerical variables: mean, median, range, quartiles, standard deviation, skewness, and kurtosis.

Visual diagnosis: histograms, box plots, scatter plots, Q-Q plots, heatmaps, and maps.

3. Test Differences and Associations

Use hypothesis tests to assess whether observed differences or associations are unlikely to result from sampling variation alone.

One mean: z-test or one-sample t-test.

Two independent means: independent-samples t-test.

Two related means: paired-samples t-test.

Three or more means: ANOVA; use MANOVA for several continuous outcomes.

Categorical association: chi-square test.

Variance or nested-model comparison: F-test.

4. Model Continuous Outcomes

These methods explain or predict a numerical dependent variable.

Linear relationships: simple or multiple linear regression.

Nonlinear relationships: polynomial regression or generalized additive models.

Outliers or unequal variance: robust regression.

Effects at different points of the outcome distribution: quantile regression.

Nested observations: multilevel or hierarchical regression.

Association without a designated outcome: Pearson, Spearman, Kendall, or canonical correlation.

5. Model Categorical and Count Outcomes

The model must reflect whether the outcome is binary, unordered, ordered, or a count.

Binary outcome: logistic or probit regression.

Unordered outcome with three or more categories: multinomial logit or probit.

Ordered outcome: ordered logit or probit.

Count outcome: Poisson regression.

Overdispersed count outcome: negative binomial regression.

Excess zeros: zero-inflated or hurdle models.

6. Handle Limited Outcomes and Sample Selection

Specialised models are needed when outcomes are censored or truncated, when many observations are zero, or when the outcome is observed only for a non-random subgroup.

Censored outcome: Tobit or censored regression.

Truncated sample: truncated regression.

Zero participation followed by a positive amount: two-part or Cragg model.

Non-randomly observed outcome: Heckman selection regression, which jointly models selection and the outcome equation to correct sample-selection bias.

7. Address Endogeneity and Causal Questions

Use these methods when an explanatory variable is correlated with unobserved determinants of the outcome, or when the objective is to examine causal pathways rather than association alone.

Endogenous predictor with a valid instrument: instrumental variables or two-stage least squares.

Endogenous treatment or regressor: control-function or endogenous-treatment models.

Mechanisms and conditional effects: mediation, moderation, and path analysis.

8. Reduce Dimensions and Model Latent Constructs

These methods simplify complex datasets or represent concepts that cannot be measured directly.

Reduce correlated variables: principal component analysis.

Discover latent factors: exploratory factor analysis.

Confirm a proposed factor structure: confirmatory factor analysis.

Group similar observations: cluster analysis.

Classify observations into known groups: discriminant analysis.

Estimate linked measurement and structural relationships: structural equation modelling, using multiple observed indicators and latent constructs in one system.

9. Analyse Efficiency and Productivity

Efficiency models compare observed production or cost performance with an estimated best-practice frontier.

Stochastic frontier analysis: suitable for cross-sectional or panel data with a continuous output, cost, or profit measure and relevant inputs. It separates random statistical noise from one-sided technical or cost inefficiency.

Production frontier: estimates technical efficiency in transforming inputs into output.

Cost or profit frontier: estimates cost efficiency or profit efficiency relative to best practice.

10. Account for Spatial, Hierarchical, and Repeated Dependence

Standard methods may be misleading when nearby locations influence one another, observations are nested, or the same units are measured repeatedly.

Detect spatial autocorrelation: Moran’s I or Geary’s C.

Model spatial dependence: spatial lag, spatial error, or Spatial Durbin models.

Estimate relationships that vary by location: geographically weighted regression.

Model nested units: multilevel or hierarchical models.

Model repeated units over time: panel-data models with fixed effects, random effects, or other suitable longitudinal structures.

11. Use Flexible and Predictive Models

Use these approaches when prediction, classification, uncertainty estimation, or complex pattern recognition is the main objective.

Distribution-based modelling: generalized linear models.

Probability-based inference: Bayesian methods.

Interpretable nonlinear prediction: decision trees.

Ensemble prediction: random forests and gradient boosting.

High-dimensional classification or regression: support vector machines.

Complex patterns in large datasets: neural networks.

 

 

 

 

 

Quick Method-Selection Matrix

 

 

Practical Method-Selection Checklist

 

Define the objective: description, comparison, explanation, causal inference, efficiency measurement, or prediction.

Identify the outcome: continuous, binary, nominal, ordinal, count, limited, latent, output, cost, or profit.

Identify the design: independent groups, paired observations, repeated measures, hierarchical, cross-sectional, panel, time-series, or spatial data.

Inspect data quality: assess missing values, coding, outliers, distribution shape, sample size, and measurement reliability.

Match the method: choose a technique that reflects the outcome scale, selection process, dependence structure, and analytical goal.

Check assumptions: examine independence, linearity, distributional form, equal variance, multicollinearity, identification, and model-specific conditions.

Validate and report: present diagnostics, uncertainty, effect sizes, goodness of fit, efficiency estimates, and predictive performance as appropriate.