Currently the MXM package supports numerous tests for different types of target (dependent) and predictor (independent) variables. The target variable can be of continuous, discrete, categorical and of survival type. As for the predictor variables, they can be continuous, categorical or mixed.
The testIndFisher and the gSquare tests have two things in common. They do not use a model implicitly (i.e. estimate some beta coefficients), even though there is an underlying assumed one. Secondly they are pure tests of independence (again, with assumptions required).
As for the other tests, they share one thing in common. For all of them, two parametric models must be fit. The null model containing the conditioning set of variables alone and the alternative model containing the conditioning set and the candidate variable. The significance of the new variable is assessed via a log-likelihood ratio test with the appropriate degrees of freedom. All of these tests are summarized in the below table.
Target variable | Predictor variables | Available tests |
Short explanation | Continuous | Continuous |
testIndFisher (robust) | Partial correlation | Continuous |
Continuous | testIndSpearman | Partial correlation |
Continuous | Mixed | testIndReg (robust) |
Linear regression | Continuous | Mixed |
testIndRQ | Median regression | Proportions |
Continuous | testIndFisher (robust) | Partial correlation |
after logit transformation | ||
Proportions | Continuous | |
testIndSpearman | Partial correlation | |
after logit transformation | ||
Proportions | Mixed | testIndReg(robust) |
Linear regression | ||
after logit transformation | Proportions | |
Mixed | testIndRQ | Median regression |
after logit transformation | ||
Proportions | Mixed | |
testIndBeta | Beta regression | Non negative |
Mixed | testIndIGreg | Inverse Gaussian regression |
Non negative | Mixed | censIndWR |
Weibull regression | Successes \& totals | Mixed |
testIndBinom | Binomial regression | Discrete |
Mixed | testIndPois | Poisson regression |
Discrete | Mixed | testIndZIP |
Zero Inflated | ||
Poisson regression | Discrete | |
Mixed | testIndNB | Negative binomial regression |
Factor with two | Mixed | testIndLogistic |
Binary logistic regression | levels or binary | |
Factor with more | ||
Mixed | testIndLogistic | Multinomial logistic regression |
than two levels | ||
(unordered) | ||
Factor with more than | ||
Mixed | testIndLogistic | Ordinal logistic regression |
two levels (ordered) | ||
Categorical | Categorical | |
gSquare | G-squared test of independence | Categorical |
Categorical | testIndLogistic | Multinomial logistic regression |
Categorical | Categorical | testIndLogistic |
Ordinal logistic regression | Continuous, proportions, | Mixed |
testIndSpeedglm | Linear, binary logistic | binary or counts |
or poisson gression | ||
Survival | Mixed | censIndCR |
Cox regression | Survival | Mixed |
censIndWR | Weibull regression | Survival |
Mixed | censIndER | Exponential regression |
Case-control | Mixed | testIndClogit |
Conditional logistic regression | Multivariate continuous | Mixed |
testIndMVreg | Multivariate linear regression | Compositional data |
Mixed | testIndMVreg | Multivariate linear regression |
(no zeros) | after multivariate | |
logit transformation | Longitudinal | |
Continuous | TestIndGLMM | (Generalised) linear |
mixed models | Target variable | Predictor variables |
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