Statistical and analytical models included in the cleaned comparative reference.
STATISTICAL ANALYSIS · MODELLING
Comprehensive Statistical Models.
A comparative reference to statistical models used across predictive, exploratory, inferential, correlational, probabilistic and survival analysis.
REPORT OVERVIEW
Choosing statistical models for different analytical questions.
Statistical models provide structured approaches for analysing data and examining relationships between variables. They support researchers, analysts and data scientists in identifying patterns, testing relationships, making predictions and interpreting empirical evidence.
This report compares a broad range of statistical models by analytical category, primary use, compatible data types, selection considerations and commonly used software.
Predictive, exploratory, inferential, correlational, probabilistic and survival models.
Model, category, purpose, data compatibility, suitability, selection criteria and software.
Support model selection according to the analytical question, outcome structure and characteristics of the available data.
01
STATISTICAL ANALYSIS
Comparative Table of Statistical Models.
The table below compares statistical models by their analytical role, primary application, supported data, appropriate use, selection considerations and commonly used software.
| Statistical Model | Category | Primary Use | Data Types Supported | Best For | Criteria to Choose | Tools / Software |
|---|---|---|---|---|---|---|
| Simple Linear Regression | Predictive Model | Predicts a dependent variable using a single independent variable | Continuous dependent; continuous/ordinal independent | Primary/secondary data; continuous outcomes | Linear relationship between variables; normality assumptions | SPSS, R, Python, Excel |
| Multiple Linear Regression | Predictive Model | Predicts a dependent variable using multiple independent variables | Continuous dependent; continuous/ordinal/categorical independent | Primary/secondary data; complex relationships; continuous outcomes | Multivariate data; no multicollinearity; dependent variable continuous | Stata, R, Python, SAS, SPSS |
| Logistic Regression | Predictive Model | Classifies the dependent variable into binary or categorical outcomes | Categorical dependent; continuous/categorical independent | Primary data with categorical outputs | Classification tasks; non-linear relationships | Python, R, Stata, SPSS |
| Poisson Regression | Predictive Model | Models count data and rates | Count data | Primary/secondary data; count-based outcomes | Data follows a Poisson distribution | R, Stata, SPSS |
| Decision Trees | Predictive Model | Classifies outcomes based on decision rules | Categorical or continuous dependent | Primary data; classification or regression tasks | Non-linear relationships; small to large datasets | Python, R, Weka |
| Random Forest | Predictive Model | Ensemble method combining multiple decision trees | Continuous or categorical dependent | Primary/secondary data; classification/regression | Handles high-dimensional data well | Python, R, Weka |
| Support Vector Machines (SVM) | Predictive Model | Classifies data using hyperplanes | Continuous/categorical data | Primary data; small datasets | Clear margin of separation | Python, R, MATLAB |
| Naive Bayes | Predictive Model | Probabilistic classifier based on Bayes' theorem | Categorical data | Primary/secondary data | Independence assumption between predictors | Python, R, Weka |
| K-Nearest Neighbors (KNN) | Predictive Model | Classifies data based on nearest neighbors | Continuous or categorical data | Primary data | Distance-based decision making | Python, R, Weka |
| Principal Component Analysis (PCA) | Exploratory Model | Reduces dimensionality while retaining variance | Continuous data | High-dimensional datasets | Exploratory data analysis; noise reduction | Python, R, MATLAB |
| Hierarchical Clustering | Exploratory Model | Groups data into hierarchical clusters | Continuous data | Primary/secondary data | Data with unknown groupings | Python, R, SPSS |
| K-Means Clustering | Exploratory Model | Partitions data into clusters based on centroids | Continuous data | Primary data; large datasets | Unsupervised learning tasks | Python, R, MATLAB |
| Structural Equation Modeling (SEM) | Exploratory Model | Analyses structural relationships between variables | Continuous or categorical data | Survey-based data | Complex relationships with latent variables | AMOS, R, Python |
| Latent Dirichlet Allocation (LDA) | Exploratory Model | Identifies topics in text data | Textual data | Primary/secondary data | Unsupervised learning; text-heavy datasets | Python, R |
| Time Series Analysis (ARIMA) | Predictive Model | Models temporal trends in data | Time-series data | Primary/secondary data | Data with temporal dependencies | Python, R, Stata |
| Cox Proportional Hazards | Survival Model | Analyses time-to-event data | Survival data | Medical, reliability engineering | Event-based analysis with censoring | R, Python, SAS |
| Bayesian Networks | Probabilistic Model | Represents relationships between variables probabilistically | Continuous/categorical data | Primary data | Probabilistic inference and dependencies | Python, R |
| Factor Analysis | Exploratory Model | Identifies latent variables | Continuous data | Survey and psychometric data | Reduces observed variables to latent factors | SPSS, R, Python |
| Canonical Correlation Analysis (CCA) | Exploratory / Correlational Model | Explores relationships between two sets of variables | Continuous/ordinal dependent and independent variables | Multiple predictors and outcomes; relationships between datasets | When there are multiple independent and dependent variables to correlate | R, Python, Stata |
| Multivariate Analysis of Variance (MANOVA) | Inferential Model | Analyses group differences on multiple dependent variables | Continuous dependent; categorical independent | Experimental data | Tests for differences across groups | SPSS, R, SAS |
| Mixed-Effect Models | Predictive Model | Handles fixed and random effects | Continuous or categorical data | Hierarchical data | Analyses repeated measures | R, Python, Stata |
| Discriminant Analysis | Predictive Model | Classifies observations into groups | Continuous independent; categorical dependent | Primary data | Classifies and predicts group membership | SPSS, R, Python |
| Gaussian Mixture Models | Probabilistic Model | Clusters data probabilistically | Continuous data | Unsupervised clustering tasks | — | — |
| Probit Regression | Predictive Model | Models binary outcomes based on normality | Binary dependent; continuous/ordinal/categorical independent | Binary outcomes where normal distribution of the error term is assumed | Similar to logistic regression but used where the probit specification is appropriate | Stata, R, Python |
| Ridge Regression | Predictive Model | Reduces overfitting by adding regularization | Continuous dependent; continuous/ordinal/categorical independent | High-dimensional datasets; multicollinear data | When multicollinearity exists among predictors or overfitting is a concern | Python (Scikit-learn), R, MATLAB |
| Lasso Regression | Predictive Model | Performs variable selection and regularization | Continuous dependent; continuous/ordinal/categorical independent | Feature selection in high-dimensional datasets | When feature selection is needed and overfitting is a concern | R, Python, MATLAB |
| Spearman's Rank Correlation | Correlational Model | Measures monotonic relationships between variables | Ordinal or continuous data | Non-linear relationships; ordinal data | When data is ordinal or non-normally distributed | R, Python, SPSS, Excel |
| Kendall's Tau | Correlational Model | Measures ordinal associations | Ordinal or continuous data | Small datasets; ordinal associations | When there are ties in the data and smaller sample sizes are involved | R, Python, SPSS |
| Cluster Correlation | Correlational Model | Examines correlations within and between clusters of data | Grouped data | Hierarchical or clustered datasets | When data is grouped or nested and within/between-group correlations are of interest | R, Python, MATLAB |
| Negative Binomial Regression | Predictive Model | Handles overdispersed count data | Count dependent; continuous/categorical independent | Overdispersed count data | When count data shows overdispersion (variance greater than mean) | R, Stata, SAS, Python |
| Multinomial Logistic Regression | Predictive Model | Predicts outcomes with more than two categories | Categorical dependent; continuous/ordinal/categorical independent | Multiclass categorical outcomes | When the dependent variable has more than two categories | Stata, SPSS, R, Python |
| Hierarchical Linear Modeling (HLM) | Predictive Model | Models nested data structures | Continuous/ordinal dependent; nested data structures | Multilevel datasets such as students within classes or employees within departments | When observations are nested and within-group dependencies must be modelled | R, HLM Software, Stata, SPSS |
Model selection should follow the research question, measurement level, structure of the dependent variable, characteristics of the data and assumptions of the proposed analytical technique.
02
MODEL FAMILIES
Different models answer different analytical questions.
The models in this reference span several analytical families. Predictive approaches dominate the collection, while exploratory, correlational, probabilistic, inferential and survival models address different forms of empirical questions.
The presence of a model in a particular family should be read as a practical organising device rather than a substitute for evaluating the assumptions and purpose of the individual statistical technique.
PUBLICATION NOTE
A comparative statistical reference.
This publication is designed as a practical starting point for comparing analytical methods. A statistical model should ultimately be selected according to the research objective, data structure, measurement properties and assumptions relevant to the individual analysis.
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