by Begarving Arthur
Explore key statistical models and their uses in predictive, descriptive, and exploratory analyses.
Statistical models are fundamental tools for analyzing data and understanding the relationships between variables. They enable researchers, analysts, and data scientists to make informed decisions by modeling the underlying patterns in data.
From simple regression techniques to complex multivariate models, each statistical approach has its specific use case and application scenario. By selecting the right model, you can accurately interpret results and address real-world challenges effectively.
Below is a comprehensive table of 28 statistical models, categorized by type, their primary use, data compatibility, and tools/software commonly used to implement them.
| Statistical Model | Category | Primary Use | Data Types Supported | Best For These Data Types | Criteria to Choose | Tools/Software |
|---|---|---|---|---|---|---|
| Simple Linear Regression | Predictive Model | Predicts 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 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 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 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 | Analyzes 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 | Analyzes 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 Model | Analyzes relationships between two sets of variables | Continuous data | Primary/secondary data | Identifies cross-variable correlations | R, Python |
| Multivariate Analysis of Variance (MANOVA) | Inferential Model | Analyzes 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 | Analyzes 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 error term is assumed | Similar to logistic regression but chosen when probabilities near 0 or 1 need precise handling | 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; model 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 |
| Canonical Correlation Analysis (CCA) | Correlational Model | Explores relationships between two sets of variables | Continuous/ordinal dependent and independent | Multiple predictors and outcomes; understanding relationships between datasets | When there are multiple independent and dependent variables to correlate | R, Python, Stata |
| 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 correlations within/between groups 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 > 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 (e.g., students in classes, employees in departments) | When data is nested or hierarchical, and dependencies within groups need to be modeled | R, HLM Software, Stata, SPSS |
| Probit Regression | Predictive Model | Models binary outcomes based on normality | Binary dependent; continuous/ordinal/categorical independent | Binary outcomes where normal distribution of error term is assumed | Similar to logistic regression but chosen when probabilities near 0 or 1 need precise handling | Python, R, Stata |
| Canonical Correlation Analysis (CCA) | Correlational Model | Explores relationships between two sets of variables | Continuous/ordinal dependent and independent | Multiple predictors and outcomes; understanding relationships between datasets | When there are multiple independent and dependent variables to correlate | Python, R, Stata |
| Negative Binomial Regression | Predictive Model | Handles overdispersed count data | Count dependent; continuous/categorical independent | Overdispersed count data | When count data shows overdispersion (variance > mean) | Python, R, SAS |
