View Full Table | Close Full ViewTable 1.

Listing and descriptive statistics of cohort-level and feedlot-year-level explanatory variables available for model selection and assessment of sources of variance heterogeneity

 
Variable % of cohorts (clusters) Mean SD Median Range (minimum to maximum)
Cohort-level variables
    No. of cohorts included for analysis (clusters) 100 (n = 24,050)
    Arrival Year
        2005 51.9
        2006 48.1
    Season
        Winter 23.1
        Spring 23.7
        Summer 27.8
        Fall 25.4
    Days on feed, days 164 51 160 1 to 395
    Cohort size, cattle 153 88 125 50 to 1659
    Gender
        Steers 55.1
        Heifers 44.9
    Mean arrival BW, kg 308.6 55.1 314.0 181.0 to 408.0
Feedlot-year-level variables
    No. of feedlot-year clusters 100 (n = 50)
    Steer cohorts, % of total cohorts per feedlot-year cluster 75.6 16.9 83.5 38.4 to 93.5
    Feedlot size (No. of cattle per feedlot per year), cattle 86,003 32,625 80,423 1954 to 139,320
    Mean arrival BW per feedlot-year cluster, kg 308.5 31.4 318.0 226.0 to 359.0



View Full Table | Close Full ViewTable 2.

Details of the forward model selection strategy implemented on variances for ADG of feedlot cattle, both at the cohort level (Steps 1 and 2) and at the feedlot-year level (Step 3)1

 
DIC difference
Factors entering the model Relative to Null model Relative to model in preceding step
Null model consisting of: 0
    Fixed effects on the mean-model specification:
        Cohort size (in quartiles), mean arrival BW class, gender, feedlot size (in quartiles), arrival season, and year
    Random effect of feedlot-year cluster on the mean model specification
Step 1:
    Selection of fixed effects (i.e., τe) on the cohort-level variance
        1.1 Cohort size (in quartiles) −198 −198
        1.2 Days on feed (in quartiles) −368 −170
        1.3 Season −440 −72
        1.4 Weight class −492 −52
        No additional effects entered the model
Step 2:
    Selection of random effects (i.e., ve) on the cohort-level variance
        2.1 Clustering effect of feedlot-year −2904 −2412
Step 3:
    Selection of fixed effects (i.e., τu) on the feedlot-year-level variance
        No effect entered the model
1Selection of fixed and random effects into the model was based on deviance information criterion (DIC) differences exceeding 7, following Spiegelhalter et al. (2002).



View Full Table | Close Full ViewTable 3.

Posterior inference on sources of heterogeneous variances for ADG in commercial feedlot cattle, including marginal posterior means (PM), posterior standard deviations (PSD), 95% greatest posterior density intervals (HPD), and effective sample size (ESS) on feedlot-year-level (i.e., cluster; ) and cohort-level (i.e., ) variances.

 
Variance components (kg2) PM PSD 95% HPD ESS
Feedlot-year-level variance
    Overall1 0.0190 0.0043 0.0114, 0.0276 197,732
Cohort-level variances
Fixed effects τe
    Cohort size
        50 to 87 cattle 0.0333a 0.0033 0.0274, 0.0398 1296
        88 to109 cattle 0.0267b 0.0026 0.0221, 0.0320 1280
        110 to 166 cattle 0.0238c 0.0023 0.0197, 0.0285 1271
        >167 cattle 0.0240c 0.0024 0.0198, 0.0287 1128
    Season
        Winter 0.0235d 0.0023 0.0194, 0.0282 1266
        Spring 0.0263e 0.0026 0.0217, 0.0315 1296
        Summer 0.0303f 0.0030 0.0251, 0.0363 1282
        Fall 0.0273e 0.0027 0.0225, 0.0326 1177
    Days on feed
        1 to 156 d 0.0347g 0.0034 0.0286, 0.0417 1496
        157 to183 d 0.0250h 0.0025 0.0205, 0.0298 1396
        184 to 216 d 0.0230i 0.0023 0.0190, 0.0276 1272
        217 to 395 d 0.0256h 0.0025 0.0210, 0.0306 1079
    Arrival BW
        181 to 226 kg 0.0221j 0.0023 0.0180, 0.0268 1510
        227 to 272 kg 0.0243k 0.0024 0.0200, 0.0291 1377
        273 to 317 kg 0.0292l 0.0028 0.0241, 0.0349 1271
        318 to 362 kg 0.0289l 0.0028 0.0238, 0.0346 1184
        >362 kg 0.0302l 0.0030 0.0250, 0.0363 1078
Random effects ve between feedlot-year clusters
    Coefficient of variation CVe 0.6579 0.1770 0.4185, 0.9575 3152
a–lWithin a fixed effect factor, marginal means with different superscripts (a−c: P < 0.001 d−f: P < 0.0001 g−i: P < 0.01 j−l: P < 0.05) indicate levels that differ from each other.
1No multifactorial heterogeneity was inferred for ; i.e., .