Vuong Test for Non-Nested Models

The Vuong test compares two non-nested likelihood models fitted to the same outcome by standardizing the mean of their pointwise log-likelihood differences, with optional AIC or BIC corrections for model size.

Vuong 검정은 같은 결과변수에 맞춘 두 비내포 우도모형의 관측별 로그우도 차이를 표준화해, 어느 모형이 자료에 더 가까운지 판정하며 AIC·BIC 보정판도 함께 냅니다.

Is a zero-inflated Poisson model better than a standard Poisson model for my count data?

횟수 자료에 일반 포아송과 영과잉 포아송 중 어느 모형이 더 맞는지 검정할 수 있나요?

The Vuong test fits both models, takes each observation's log-likelihood difference and divides its mean by its standard error, giving a z statistic. A large positive value favours the first model, a large negative value favours the second, and values near zero mean the data cannot tell them apart.

When to use Vuong Test for Non-Nested Models

• You must choose between two models that are not special cases of each other, such as logit versus probit.
• You want a formal comparison of a count model with its zero-inflated version alongside AIC.
• Both models are fitted by maximum likelihood to the same observations and outcome.

When to use something else

• One model is a restricted version of the other with an interior parameter (for example Poisson inside negative binomial); use a likelihood-ratio test.
• You only need predictive accuracy on new data; use cross-validated scores or information criteria.

Assumptions and requirements

• Independent observations with the same outcome under both models.
• Both models are estimated by maximum likelihood on identical rows.
• The pointwise log-likelihood differences have positive variance (the models are distinguishable).

What the analysis reports

• Raw, AIC-corrected and BIC-corrected Vuong z statistics
• Two-sided and one-sided p values with the favoured model
• Log-likelihood, number of parameters and AIC of each model
• Mean and standard deviation of the pointwise differences

How to report it

A Vuong test comparing the Poisson model with the zero-inflated Poisson model (N = [value]) gave V = [value], p = [value] (BIC-corrected V = [value]), favouring the [model].

Related methods

• Zero Inflated Poisson Regression
• Likelihood Ratio Test
• Akaike Information Criterion

Run Vuong Test for Non-Nested Models on Quorant