Description Usage Arguments Details Value Note References See Also Examples

Extracts additive genetic, non-additive genetic, and maternal variance components
from a linear mixed-effect model using the *lmer* function of the *lme4* package.
Model random effects are dam, sire, dam by sire, and any additional fixed and/or random effects.

1 | ```
observLmer3(observ, dam, sire, response, remain, ml = F, iter = 1000)
``` |

`observ` |
Data frame of observed data. |

`dam` |
Column name containing dam (female) parent identity information. |

`sire` |
Column name containing sire (male) parent identity information. |

`response` |
Column name containing the offspring (response) phenotype values. |

`remain` |
Remaining formula using |

`ml` |
Default is FALSE for restricted maximum likelihood. Change to TRUE for maximum likelihood. |

`iter` |
Number of iterations for computing the parametric bootstrap significance value for any fixed effects. |

Extracts the dam, sire, dam, dam by sire, and residual variance components.
Extracts any additional fixed effect and random effect variance components. The fixed-effect variance
component is as a single group using the method described by Nakagawa and Schielzeth (2013).
Calculates the total variance component. Calculates the additive genetic, non-additive genetic, and
maternal variance components (see Lynch and Walsh 1998, p. 603).
Significance values for the random effects are determined using likelihood ratio tests (Bolker et al. 2009).
Significance values for any fixed effects are determined using likelihood ratio tests and a parametric
bootstrap method (Bolker et al. 2009) from the *mixed* function of the *afex* package.

A list object containing the raw variance components, the variance components as a percentage of the total variance component. Contains the difference in AIC and BIC, likelihood ratio test Chi-square and p-value for random and/or fixed effects. Also contains the parametric bootstrap Chi-square and p-value for any fixed effects.

Maximum likelihood (ML) estimates the parameters that maximize the likelihood of the observed data and has the advantage of using all the data and accounting for non-independence (Lynch and Walsh 1998, p. 779; Bolker et al. 2009). On the other hand, ML has the disadvantage of assuming that all fixed effects are known without error, producing a downward bias in the estimation of the residual variance component. This bias can be large if there are lots of fixed effects, especially if sample sizes are small. Restricted maximum likelihood (REML) has the advantage of not assuming the fixed effects are known and averages over the uncertainty, so there can be less bias in the estimation of the residual variance component. However, REML only maximizes a portion of the likelihood to estimate the effect parameters, but is the preferred method for analyzing large data sets with complex structure.

Bolker BM, Brooks ME, Clark CJ, Geange SW, Poulsen JR, Stevens MHH, White J-SS. 2009. Generalized linear mixed models: a practical guide for ecology and evolution. Trends in Ecology and Evolution 24(3): 127-135. DOI: 10.1016/j.tree.2008.10.008

Lynch M, Walsh B. 1998. Genetics and Analysis of Quantitative Traits. Sinauer Associates, Massachusetts.

Nakagawa S, Schielzeth H. 2013. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution 4(2): 133-142. DOI: 10.1111/j.2041-210x.2012.00261.x

1 2 3 4 5 | ```
data(chinook_length) #Chinook salmon offspring length
#just a few iterations for the p-value of fixed effect
length_mod3<- observLmer3(observ=chinook_length,dam="dam",sire="sire",response="length",
remain="egg_size + (1|tray)",iter=5)
length_mod3
``` |

```
[1] "2019-09-10 16:01:03 UTC"
Formula (the first argument) converted to formula.
Numerical variables NOT centered on 0: egg_size
If in interactions, interpretation of lower order (e.g., main) effects difficult.
REML argument to lmer() set to FALSE for method = 'PB' or 'LRT'
Fitting 2 (g)lmer() models:
[boundary (singular) fit: see ?isSingular
.boundary (singular) fit: see ?isSingular
.]
Obtaining 1 p-values:
[boundary (singular) fit: see ?isSingular
boundary (singular) fit: see ?isSingular
boundary (singular) fit: see ?isSingular
boundary (singular) fit: see ?isSingular
boundary (singular) fit: see ?isSingular
boundary (singular) fit: see ?isSingular
boundary (singular) fit: see ?isSingular
boundary (singular) fit: see ?isSingular
.]
boundary (singular) fit: see ?isSingular
refitting model(s) with ML (instead of REML)
Time difference of 3.101615 secs
Warning messages:
1: 'args.test' is deprecated; use 'args_test' instead
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.00223238 (tol = 0.002, component 1)
3: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.00427998 (tol = 0.002, component 1)
4: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.00239063 (tol = 0.002, component 1)
$fixed
effect variance percent Chi.sq p.value
1 egg_size NA NA 3.273533 0.2
2 Fix_Tot 0.05967763 5.660252 NA NA
$LRT.fixed
term d.AIC d.BIC Chi.sq p.value
1 egg_size 1.273533 -3.824842 3.273533 0.07040583
$random
effect effect2 variance percent
1 dam:sire (Intercept) 1.788027e-01 1.695892e+01
2 tray (Intercept) 1.197903e-01 1.136176e+01
3 sire (Intercept) 7.596946e-09 7.205486e-07
4 dam (Intercept) 1.461673e-01 1.386355e+01
$LRT.random
term d.AIC d.BIC Chi.sq p.value
1 (1 | dam) 14.154638 9.056262 16.15464 5.837547e-05
2 (1 | sire) -2.000001 -7.098377 0.00000 1.000000e+00
3 (1 | dam:sire) 141.433952 136.335577 143.43395 4.724439e-33
4 (1 | tray) 122.909890 117.811514 124.90989 5.325910e-29
$other
component variance percent
1 Residual 0.5498902 52.15551
2 Total 1.0543281 100.00000
$calculation
component variance percent
1 additive 3.038778e-08 2.882194e-06
2 nonadd 7.152107e-01 6.783569e+01
3 maternal 1.461673e-01 1.386355e+01
```

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