Multikolinearno

Multikolinearno, commonly referred to in English as multicollinearity, describes a situation in regression analysis where two or more predictor variables are highly linearly related. When predictors are nearly a linear combination of others, the regression model struggles to identify unique contributions from each variable, and coefficient estimates become unstable.

Causes of multikolinearno include strong correlations among predictors, redundancy from including both a variable and its transformed or derived counterparts (for example a variable and its square in a limited range), and the use of many dummy variables for a categorical feature, which can produce near-perfect or perfect collinearity.

The main consequences are inflated standard errors of the estimated coefficients, reduced statistical power to detect effects, and coefficients that are sensitive to small changes in the data or model specification. This makes it difficult to interpret the independent effect of each predictor.

Detection methods commonly rely on the variance inflation factor (VIF) and tolerance. A VIF substantially greater than 5 or 10, or a tolerance near zero, indicates problematic multicollinearity. Additional diagnostics include the condition number of the design matrix and the examination of correlation matrices among predictors.

Remedies include removing or combining correlated predictors, applying dimensionality reduction such as principal component analysis, and using regularization techniques like ridge or lasso regression. Centering or standardizing variables can help in some cases, and increasing sample size may mitigate effects. It is important to distinguish multikolinearno from perfect multicollinearity, where the model matrix is singular and estimation becomes impossible without altering the model.