Estimation and prediction ability of linear and threshold models for yearling breed quality score (BQ) and navel development score at weaning (WN) and yearling (YN), considering variances, heritabilities, and rank correlations based on the breeding values predicted for bulls, were compared. Furthermore, it was determined whether BQ, WN, and YN are genetically associated with growth traits (BWG: birth to weaning weight gain, WH: weaning height, WYG: weaning to yearling weight gain, YH: yearling height) to field data of Nelore cattle. For BQ, similar heritabilities were estimated using linear (0.14 ± 0.01) and threshold (0.15 ± 0.02) models. For navel development scores, higher heritability was estimated with threshold (WN 0.22 ± 0.03; YN 0.42 ± 0.03) rather than linear (WN 0.16 ± 0.01; YN 0.29 ± 0.01) models. Rank correlations between sires breeding values predicted for visual scores with linear and threshold models ranging from 0.53 to 0.98, indicating that different sires would be selected using these models, mainly for higher selection intensities. The BQ showed little genetic variability and was not associated with WH and YH. However, low and positive genetic correlations were obtained between BQ with BWG (0.27 ± 0.02) and WYG (0.25 ± 0.02). In general, they are expected low genetic gains for BQ as correlated response to selection based on any of the growth traits studied. The WN showed higher genetic correlation with BWG (0.63 ± 0.02) and WH (0.53 ± 0.02) rather than WYG (-0.06 ± 0.02) and YH (0.26 ± 0.02), indicating that selection for increased growth at weaning (height and weight gain) should lead to longer and most pendulous navels at this age. Weak genetic correlations were obtained between yearling navel and growth traits.