Modern statistical techniques

Modern statistical techniques

• 1.
  Relaxation of aconstraint / assumption (1) Gaussian conditional distribution of the response (4) Independence of observations (within cluster, subject, level) (7) Conditional distribution of the response comes from the one-parameter exponential family (10) No outliers and other distributional issues (2) Gaussian distribution of the random effects (5) Direct linearity in parameters. Models relationship between the conditional (w.r.t. predictor) E(response) and the linear predictor. Unrelated mean and variance. (8) Uncorrelated independent variables (11) Assumed / known conditional distribution of the response (3) Homoscedasticity (homogeneity of variance) (6) Indirect linearity in parameters. Models relationship between the function of conditional (w.r.t. predictor) E(response) and the linear predictor. (9) Non-truncated, non-censored response (12) Missing Completely At Random (MCAR) (13) The residual covariance must be specified correctly (14) independent variables have been measured or observed without error (15) Population averaged parameters (16) Proportional odds General Linear Model (via OLS) (linear, linearized, polynomial regression, ANCOVA) General Linear Model via Weighted OLS  Generalized Least Square (GLS) Generalized Linear Model (GLM) (e.g. binomial: logistic/probit, gamma, Poisson, ordinal (proportional odds) & multinomial logistic, log-linear, fractional logistic regression) Vector Generalized Linear Model (VGLM) (e.g. , 0-altered Poisson, positive Poisson, negative binomial, beta regression, 0- 1-inflated beta regression), partial proportional odds (PPO) Generalized Estimating Equations (GEE) GEE1= First Order, GEE2 = Second order Weighted Generalized Estimating Equations (WGEE) {Generalized [Additive] [Non-Linear] } (Robust) Mixed-Effect Model LMM, (V)GLMM, GNMM, VGAMM Generalised Additive Models for Location Scale and Shape (GAMLSS) (Vector) Generalized Additive Model ([V] GAM) General Non-Linear Model via Least Square (GNLS) Generalized Non-Linear Model (GNM) Generalized Additive Main effects and Multiplicative Interaction (GAMMI) Alternating Logistic Regression (ALR) Spatial Generalised Linear Mixed Models (SGLMM) Quantile Linear Model Quantile Additive Linear Model Robust Models via M-estimators (GLM, GAM) Censored Regression 1-/2-sided Tobin’s model (tobit regression) Truncated Gaussian Response Model Linear Ordering Isotonic Regression Censored Models for Time-To-Event analysis (Survival ) e.g. Cox (Proportional-hazard), Counting models (Anderson-Gill, Prentice-Williams-Peterson, Wei-Lin- Weissfeld), Competing risks (Fine-Gray), (Shared/Joint) Frailty models Accelerated Failure Time (AFT), Parametric survival (Weibull, Exponential, Gompertz, gamma, Coale-McNeil), etc. Regularization (e.g. Ridge (Tikhonov), LASSO, elastic net) (V)GAM, GLM,… 1 2 3 3 5 6 6 6 6 6 7 7 4 4 4 8 9 9 10 10 11 12 12 combines 7 Additive Main effects and Multiplicative Interaction (AMMI) 13 Errors-In-Variables Models e.g. via Total Least Squares (TLS) (e.g. Deming regression) Passing-Bablock Regression 14 14 10 14 5 3 Generalized Ordered Logit 16 Special case Generalized Linear Latent And Mixed Models (GLLAMM) Special cases: Item-Reponse Theory models (IRT), Generalized Linear Mixed Models (GLMM), Factor Models, Structural Equation Models (SEM), Latent Class Models Special case Dispersion Models (e.g. simplex regression)