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The discrepancy calculation for glmer must be wrong.  All variance
component estimates are being driven to zero.
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Approximate standard errors and correlations for the fixed effects
parameters in nlmer and glmer models.  Should there be a general
calculation of the information matrix?
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Find out why there is a .p at the end of the model names in the
printed value of anova with multiple arguments.
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Collapse repeated grouping factors and correspondingly modify the
ranef and coef methods.
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Check the calculation of the conditional variances of the random effects.
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Add an element to the deviance slot to hold sigma or log(sigma).  The
interpretation will be that an NA value means to use the conditional
estimate of the scale parameter.  For a generalized linear mixed model
without a scale parameter set sigma = 1 (or log(sigma) = 0) and put
constraints on the parameter so that it is not estimated.

Upon convergence replace that element with the conditional estimate in
models where it has been profiled out.
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Consider the steps in reimplementing AGQ.  First you need to find the
conditional modes, then evaluate the conditional variances, then step
out according to the conditional variance, evaluate the integrand
relative to the step.

The paper by Sophia Rabe-Hesketh et al describes a spherical form
of the Gauss-Hermite quadrature formula.  Look that up and use it.

Because the Gauss-Hermite quadrature is formed as a sum, it is
necessary to divide the contributions to the deviance according to
the levels of the random effects.  This means that it is only
practical to use AGQ when the response vector can be split into
sections that are conditionally independent. As far as I can see
this will mean a single grouping factor only.
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Allow for a matrix of responses in lmer so multiple fits can be
performed without needing to regenerate the model matrices.
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Modify the one-argument form of the anova method for lmer objects (yet
  again) to calculate the F ratios.  It is the df, not the ratio that
  is controversial.
Should there be an extractor function for the mean square error?  If
  so, what should it be called?
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Determine what a "coef" function should do for multiple, possibly
  non-nested, grouping  factors.
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Determine why the names of the components of the values of
the ranef and coef extractor methods are not printed.
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- add nicer (more realistic?) pedigree examples and tests

- document print(<mer>) including an example  print(<lmer>, corr = FALSE)