I got completely different results from lmer() and lme()! Just look at the coefficients' std.errors. Completely different in both cases. Why is that and which model is correct?

`> mix1c = lmer(logInd ~ 0 + crit_i + Year:crit_i + (1 + Year|Taxon), data = datai) > mix1d = lme(logInd ~ 0 + crit_i + Year:crit_i, random = ~ 1 + Year|Taxon, data = datai) > > summary(mix1d) Linear mixed-effects model fit by REML Data: datai AIC BIC logLik 4727.606 4799.598 -2351.803 Random effects: Formula: ~1 + Year | Taxon Structure: General positive-definite, Log-Cholesky parametrization StdDev Corr (Intercept) 9.829727e-08 (Intr) Year 3.248182e-04 0.619 Residual 4.933979e-01 Fixed effects: logInd ~ 0 + crit_i + Year:crit_i Value Std.Error DF t-value p-value crit_iA 29.053940 4.660176 99 6.234515 0.0000 crit_iF 0.184840 3.188341 99 0.057974 0.9539 crit_iU 12.340580 5.464541 99 2.258301 0.0261 crit_iW 5.324854 5.152019 99 1.033547 0.3039 crit_iA:Year -0.012272 0.002336 2881 -5.253846 0.0000 crit_iF:Year 0.002237 0.001598 2881 1.399542 0.1618 crit_iU:Year -0.003870 0.002739 2881 -1.412988 0.1578 crit_iW:Year -0.000305 0.002582 2881 -0.118278 0.9059 Correlation: crit_A crit_F crit_U crit_W cr_A:Y cr_F:Y cr_U:Y crit_iF 0 crit_iU 0 0 crit_iW 0 0 0 crit_iA:Year -1 0 0 0 crit_iF:Year 0 -1 0 0 0 crit_iU:Year 0 0 -1 0 0 0 crit_iW:Year 0 0 0 -1 0 0 0 Standardized Within-Group Residuals: Min Q1 Med Q3 Max -6.98370498 -0.39653580 0.02349353 0.43356564 5.15742550 Number of Observations: 2987 Number of Groups: 103 > summary(mix1c) Linear mixed model fit by REML Formula: logInd ~ 0 + crit_i + Year:crit_i + (1 + Year | Taxon) Data: datai AIC BIC logLik deviance REMLdev 2961 3033 -1469 2893 2937 Random effects: Groups Name Variance Std.Dev. Corr Taxon (Intercept) 6.9112e+03 83.13360 Year 1.7582e-03 0.04193 -1.000 Residual 1.2239e-01 0.34985 Number of obs: 2987, groups: Taxon, 103 Fixed effects: Estimate Std. Error t value crit_iA 29.0539403 18.0295239 1.611 crit_iF 0.1848404 12.3352135 0.015 crit_iU 12.3405800 21.1414908 0.584 crit_iW 5.3248537 19.9323887 0.267 crit_iA:Year -0.0122717 0.0090916 -1.350 crit_iF:Year 0.0022365 0.0062202 0.360 crit_iU:Year -0.0038701 0.0106608 -0.363 crit_iW:Year -0.0003054 0.0100511 -0.030 Correlation of Fixed Effects: crit_A crit_F crit_U crit_W cr_A:Y cr_F:Y cr_U:Y crit_iF 0.000 crit_iU 0.000 0.000 crit_iW 0.000 0.000 0.000 crit_iA:Yer -1.000 0.000 0.000 0.000 crit_iF:Yer 0.000 -1.000 0.000 0.000 0.000 crit_iU:Yer 0.000 0.000 -1.000 0.000 0.000 0.000 crit_iW:Yer 0.000 0.000 0.000 -1.000 0.000 0.000 0.000 > `

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#### Best Answer

`lmer`

uses Laplace approximation, when the whole normal distribution of the random effect is approximated at its mode. This approximation is known to produce the estimates of the variance components that are biased down. `lme`

uses a more thorough approximation via Gaussian quadrature approximation, but I neither know the default number of integration points nor the way to manipulate this number.

Note also that `lmer`

produced a correlation of the random effects (the intercept vs. year) of -1. That's very bad, and is indicative of numeric problems. It hit some sort of a ridge in its approximation of the likelihood that it could not overcome (no wonder, given that this approximation is quite poor). `lme`

did a somewhat better job, and came up with a correlation of 0.619. If you really have a year, as in, 2010, 2011, 2012, that's a very bad idea for mixed models, where high multicollinearity between factors may mean poor numeric stability and long convergence. You would have been much better off converting it to `time`

centered near zero, rather than near 2010.

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