The following table lists common “portmanteau” names for linear models. Note that different traditions/disciplines might use one particular name more often than the others.

My usual recommendation is to move away from using specific names like “logistic regression” or “mixed-effects models” and instead just specify what kind of components your linear model has (see the Description column in the table).

Formula | Description | Names |
---|---|---|

`lm(y ~ x)` |
Linear model with one predictor `x` using a Gaussian distribution for the outcome variable `y` |
simple linear regression, simple linear model |

`lm(y ~ x + z + ...)` |
Linear model with two predictors or more using a Gaussian distribution for the outcome variable `y` |
multiple linear regression, multiple linear model |

`glm(y ~ x + ..., family = "binomial")` |
Linear model with one or more predictors using a Bernoulli distribution for the outcome variable `y` |
logistic regression, binomial regression, general(ised) linear model |

`lmer(y ~ x + ... + (1 | z))` |
Linear model with one or more predictors, including one or more random intercepts, using a Gaussian distribution for the outcome variable `y` . |
mixed-effects models, nested models, hierarchical models, multilevel models, cross-effects models (plus combinations of those and “linear” or “regression”) |

`lmer(y ~ x + ... + (w | z))` |
Linear model with one or more predictors, including one or more random intercepts and one or more random slopes, using a Gaussian distribution for the outcome variable `y` . |
Same as above. Sometimes “random-slope models” |

`glmer(y ~ x + ... + (w | z), family = "binomial")` |
Linear model with one or more predictors, including one or more random intercepts and one or more random slopes, using a Bernoulli distribution for the outcome variable `y` . |
Same as above, but includes “logistic”, “binomial” or “general(ised)” in the name |

`glm(..., family = "poisson")` |
Linear model with one or more predictors, including one or more random intercepts and one or more random slopes, using a Poisson distribution for the outcome variable `y` . |
Same as above but includes “Poisson” in the name |

**Note**: When specifying the binomial family in `glmer()`

, the Bernoulli family is selected automatically under the hood