Description Usage Arguments Details Value Note Author(s) References See Also Examples

`mhglm`

is used to fit a moment hierarchical generalized linear model.

1 2 3 4 5 6 7 8 9 10 | ```
mhglm(formula, family = gaussian, data, weights, subset,
na.action, start = NULL, etastart, mustart, offset,
control = list(), model = TRUE, method = "mhglm.fit",
x = FALSE, z = FALSE, y = TRUE, group = TRUE,
contrasts = NULL)
mhglm.fit(x, z, y, group, weights = rep(1, nobs),
start = NULL, etastart = NULL, mustart = NULL,
offset = rep(0, nobs), family = gaussian(),
control = list(), intercept = TRUE)
``` |

```
formula, family, data, weights, subset, na.action, start, etastart,
mustart, offset, model, contrasts, intercept
``` |
These arguments
are analogous to the similarly-named arguments for the |

`control` |
a list of parameters for controlling the fitting
process. For |

`method` |
the method to be used in fitting the model. The default
method |

`x, z, y, group` |
For For |

These functions are analogues of `glm`

and
`glm.fit`

, meant to be used for fitting hierarchical
generalized linear models. A typical predictor has the form
`response ~ terms + (reterms | group)`

where
`response`

is the (numeric) response vector, `terms`

is a
series of terms which specifies a linear predictor for
`response`

, `reterms`

is a series of terms with random
coefficients (effects), and `group`

is a grouping factor; observations
with the same grouping factor share the same random effects.

Currently, only one random effect term is allowed, along with a single
level of hierarchy; random effect terms of the form
`reterms | g1/.../gQ`

are not supported.

`mhglm`

returns an object of class inheriting from `"mhglm"`

.

The function `summary`

can be used to obtain or print a summary
of the results.

The generic accessor functions `fixef`

, `ranef`

,
`VarCorr`

, `sigma`

, `fitted.values`

and
`residuals`

can be used to extract various useful features of the
value returned by `mhglm`

.

If the moment-based random effect covariance is not positive-semidefinite, then a warning will be issued, and a projection of the estimate to the positive-semidefinite cone will be used instead.

Patrick O. Perry

Perry, P. O. (2015) "Fast Moment-Based Estimation for Hierarchical Models", Preprint.

`terms.mhglm`

, `model.matrix.mhglm`

, and
`predict.mhglm`

for `mhglm`

methods, and the
generic functions `fitted.values`

, `residuals`

,
`summary`

, `vcov`

, and `weights`

.

Generic functions `fixef`

, `ranef`

,
`VarCorr`

, and `sigma`

for features
related to mixed effect models.

`glmer`

(package lme4) for
fitting generalized linear mixed models with likelihood-based estimates.

1 2 3 4 5 6 |

```
Loading required package: nlme
Loading required package: Matrix
Attaching package: 'lme4'
The following object is masked from 'package:nlme':
lmList
Call:
mhglm(formula = Reaction ~ Days + (Days | Subject), family = gaussian,
data = sleepstudy)
Random effects:
Variance Std. Dev.
(Intercept) 565.52 23.781
Days 32.68 5.717
Fixed effects:
Estimate Std. Error t value Pr(> |t|)
(Intercept) 251.405 6.632 37.906 < 2e-16 ***
Days 10.467 1.502 6.968 1.07e-10 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 654.9)
Call:
mhglm(formula = cbind(incidence, size - incidence) ~ period +
(1 | herd), family = binomial, data = cbpp)
Random effects:
Variance Std. Dev.
(Intercept) 0.2174 0.4662
Fixed effects:
Estimate Std. Error t value Pr(> |t|)
(Intercept) -1.0555 0.2018 -5.230 1.69e-07 ***
period2 -0.8365 0.2951 -2.835 0.004582 **
period3 -0.7566 0.3182 -2.378 0.017421 *
period4 -1.1718 0.3537 -3.314 0.000921 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
```

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