In my experimental design I have 4 treatments, 3 replicates per treatment and 3 blocks. In each plot I measured whether a plant is infested or not ("Infestate" variable). This measure has been performed to 30 to 40 plants placed at the centre of the plot. Sampling has been performed weekly (variable "Data_rilievo) on the same plants, even though the sample size might vary if some plants die. Treatment does not influence plant death. Thus, I removed from the dataset the observations resulted in plant death.
I obtained the following dataset:
'data.frame': 2937 obs. of 15 variables: $ ID_pianta : chr "_Pianta_1" "_Pianta_2" "_Pianta_3" "_Pianta_4" ... $ Data_rilievo : POSIXct, format: "2023-11-14" "2023-11-14" "2023-11-14" ... $ Blocco : num 2 2 2 2 2 2 2 2 2 2 ... $ Trattamento : chr "Controllo" "Controllo" "Controllo" "Controllo" ... $ Infestate : num 1 0 0 1 0 1 0 0 1 0 ...
I opted for a mixed-effect model with treatment as fixed effect, plant ID ("ID_pianta") as random effect to account for repeated measures, and block ("Blocco") as random effect.
And this is the result
> summary(model) Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod'] Family: binomial ( logit ) Formula: Infestate ~ Trattamento + (1 | ID_pianta) + (1 | Blocco) Data: data AIC BIC logLik deviance df.resid 3835.8 3871.7 -1911.9 3823.8 2931 Scaled residuals: Min 1Q Median 3Q Max -2.1969 -1.0611 0.6139 0.8091 1.5079 Random effects: Groups Name Variance Std.Dev. ID_pianta (Intercept) 0.16880 0.4108 Blocco (Intercept) 0.09686 0.3112 Number of obs: 2937, groups: ID_pianta, 40; Blocco, 3 Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.59808 0.20650 2.896 0.003776 ** TrattamentoLavanda -0.16521 0.11116 -1.486 0.137218 TrattamentoRosmarino -0.02389 0.11000 -0.217 0.828075 TrattamentoTimo -0.37733 0.11017 -3.425 0.000615 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation of Fixed Effects: (Intr) TrttmL TrttmR TrttmntLvnd -0.266 TrttmntRsmr -0.269 0.502 TrattamntTm -0.269 0.499 0.504
I wanted also to check the predictive abilities. I used this code
library(caret) data$Infestate
Yes, you can apply a mixed-effects model for unbalanced sample sizes and repeated measures. In fact, mixed-effects models are particularly well-suited for handling such situations.
An unbalanced sample size refers to a situation where the number of observations or subjects varies across different groups or levels of the independent variable(s). A repeated measures design involves collecting multiple measurements on the same subjects over time or under different conditions.
Mixed-effects models, also known as multilevel models or hierarchical linear models, allow for the analysis of data with both fixed and random effects. The fixed effects capture the population-level relationships between the independent and dependent variables, while the random effects account for the variability within and between different groups or levels.
When dealing with unbalanced sample sizes, mixed-effects models can handle missing data by using all available data and providing valid estimates under the missing at random (MAR) assumption. The models can account for the varying number of observations across groups and adjust for the unbalanced design.
To apply a mixed-effects model to your data, you would typically specify the fixed effects (i.e., the independent variables) and the random effects (i.e., the grouping structure) in the model. The model can then estimate the fixed effects coefficients and the variance components associated with the random effects.
It's important to note that the specific software packages or programming languages you use may have different syntax or functions for fitting mixed-effects models. Commonly used software packages for mixed-effects modeling include R (with packages like lme4 or nlme), Python (with packages like statsmodels or lme4 in R via the rpy2 interface), and SAS (PROC MIXED).
It's recommended to consult the documentation or resources specific to the software you are using to learn how to implement mixed-effects models for your unbalanced sample size and repeated measures data.
I find mixed models scientifically indefensible because they make use of time-dependent sampling unit-specific probability statements that cannot be empirically investigated. My recommendation would be to instead consider a GEE model.
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