Linear mixed model formulation

Introduction

Mixed models are quite tricky, in that, while being very powerful extensions of linear models, they are somewhat difficult to conceptualize and otherwise to specify. Mixed models have, in addition to usual fixed effect combination of factors, random effects structure. These structure need to be specified in the model formula in R. While formula specification of a model is unique in it’s own respect, the formuala expression too leads to an object with differnt properties than a regular R object. Although, the complexity of formula syntax can arbitrary (constrained by classess and methods working on that), a general guideline is applicable for most of the mixed modeling utilities. These include: lme4, nlme, glmmADMB and glmmTMB.

Rice landraces of Nepal: A reflection of past

Background

This is really a brash article meant to convey exactly what title hints at. Much of the contents are translated/transliterated from “Rice Science and Technology in Nepal: A historical, socio-cultural and technical compendium”, which was published in 2017. As of now, primary authors are left uncredited, but as entries become widely accepted, original writers and publishers will be duely recognized.

Design and analysis of spit plot experiments

Split plot design

Design and fieldbook template

In a field experiment to test for effects of fungicide on crop, treatment of fungicides may be distinguised into multiple factors – based on chemical constituent, based on formulation, based on the mode of spray, etc. In a general case scenario where two former factors could be controlled, factor combinations may be organized in several different ways. When fully crossed implementation is not possible, split plot design comes to the rescue.

Layout and visualization of experimental design

Functional approach to creating and combing multiple plots

This approach highlights features of gridExtra package that allows combining multiple grob plots using function calls. We explicitly use lapply/split or similar class of purrr functions to really scale the graphics.

We load a Hybrid maize trial dataset, with fieldbook generated using agricolae::design.rcbd(). The dataset looks as shown in Table 1, after type conversion and cleaning.

(\#tab:rcbd-maize-fieldbook)Intermediate maturing hybrids with 50 entries each in 3 replicated blocks

Rep	Block	Plot	Entry	col	row	tillering	moisture1	moisture2	Ear count	Plant height
1	1	1	1	1	1		3.0	3.5	35	270
1	1	2	3	1	2		3.0	3.5	25	266
1	1	3	18	1	3		3.5	4.0	30	261
1	1	4	32	1	4		4.0	4.5	26	224
1	1	5	37	1	5		4.0	4.5	30	268
1	2	6	27	1	6		4.0	4.5	20	268
1	2	7	21	1	7		4.0	4.5	25	277
1	2	8	13	1	8		3.5	4.0	25	264

For the given dataset, we can draw on the information that Rep variable was used as field level blocking factor (Although separate, Block, variable exists, it was nested inside the Rep.) Therefore, to begin with, we ignore other spatial grouping variable. Now, since the grid graphics only requires two way represenation of plotting data, we have row and col information feeding for that.

Design and analysis of balanced randomized complete block (RCBD) experiment

Introduction

Balanced block designs are a class of randomized experimental design that contain equal number of records for a particular level of categorical variable across all blocks.

Example 1

Let us generate some data from random process mimicking a single factor process consisting of 3 levels.