DOI: 10.5061/dryad.sn02v6xbd
title: Dairy cow dry matter intake for multiverse analysis and Bradley-Terry modeling

description: The palatability of feed for dairy cows is an important consideration but
 is difficult to measure, particularly when considering more than two
 feeds. We outline how a combination of multiverse analysis and
 Bradley-Terry modeling, two methodological tools that have rarely been
 applied in dairy science, can be adapted to address this problem.
 Specifically, we propose to apply multiverse analysis as a way to consider
 a range of thresholds for how much of a mixed grass-legume (MGL) silage
 had to be consumed (as a percent of the total DMI) to be designated as
 preferred. Each threshold gives rise to a separate dataset and a
 corresponding fitted Bradley-Terry model. Bradley-Terry models attribute
 to each feed what is commonly referred to as an “ability” in the context
 of sports or other competitions but can be interpreted as palatability
 when applied to feeds. This combined approach is a way of estimating
 palatabilities that appropriately reflect the degree of preference cows
 express through their feeding behavior. It has the advantages of being
 transparent and relatively easy to implement. A possible disadvantage is
 that this method is limited to a paired comparison approach and has
 difficulties with main-effects statistical inference. We demonstrate the
 use of this methodology on an example dataset comparing MGL silages under
 different ensiling conditions and exposed to oxygen for different
 durations.
description: Both experimental setup and statistical methodology are described
 in the accompanying publication. The accompanying R script also provides
 details of the statistical methodology.
description: # Dairy cow dry matter intake for multiverse analysis and Bradley-Terry
 modeling This dataset
 originates from a study conducted at the William H. Miner Agricultural
 Research Institute (Chazy, NY) during summer 2021. Feed from two bunks
 (that is, two ensiling conditions) and from two aerobic exposure times (0
 and 48 hours) were considered, for a total of four feed types. The four
 feed types were offered to twelve heifers in a pairwise fashion (4 types =
 6 pairwise comparisons). The observations consist of the dry matter intake
 of each heifer by feed type and day. This dataset is being employed as a
 testbed for an statistical analysis approach consisting of multiverse
 analysis and Bradley-Terry modeling. ## Description of the data and file
 structure The dataset consists of a single CSV file
 (dry_matter_intake_for_multiverse_and_bt.csv). The unit of observation is
 a feed offered on a particular day to a particular cow. That is, each row
 is "half" of one pairwise comparison. There are 144 observations
 (12 heifers x 2 feeds/day x 6 days). The file contains nine columns: date
 - date in M/D/YYYY format cow.id - cow ID trmt - feed type (A0 = bunk A, 0
 hours aerobic exposure, A48 = bunk A, 48 hours aerobic exposure, B0 = bunk
 B, 0 hours aerobic exposure, B48 = bunk B, 48 hours aerobic exposure) bunk
 - bunk the feed was taken from (A or B) time - aerobic exposure time, in
 hours (0 or 48 hours) pos - position in which the feed was offered to the
 heifer (L=left, R=right) feedout.t.C - temperature (in degrees Celsius) of
 the feed at time of feeding dmi.kg.30mins - dry matter intake (in kg)
 after 30 minutes dmi.kg.3h - dry matter intake (in kg) after 3 hours No
 observations are missing. ## Code/Software Self-documented code for
 applying the proposed methodology to the dataset is in
 "multiverse_and_bt_for_palatability.R".