### INTRODUCTION

*in vivo*evaluation, whose advantage is to obtain information of the nutritional status of animals. In goats, this technique is widely applied, however the use of ultrasound to evaluate carcass in live animals has spread because it enables the identification of carcass marbling based on intramuscular fat. It is a type of data with discrete distribution in which the

*longissimus dorsi*is the main muscle for evaluation in the living animal.

### MATERIALS AND METHODS

*In vivo*evaluation of carcass was performed by means of ultrasound images captured using the apparatus Chison 600M equipped with linear transducer (13 cm) using a set of frequency 5.0 MHz.

^{2}) was measured through ultrasonographic cross-sectional images of the

*longissimus dorsi*muscle in the intercostal space between the 12th and 13th ribs. With the same image the MRE was evaluated with by assigning grades from 0 (absence of intramuscular fat) to 6 points (abundance of intramuscular fat). This visual grading scale was an adaptation of that used by [8].

*a posteriori*distribution with 4,000 samples in which inferences were performed. Values for burn-in and sampling interval were defined based on preliminary analyses in which the convergence and distribution of samples were evaluated through the POSTGIBBS1F90 program [10], which uses the Geweke diagnostic test [11] based on the Z test of average equality of the conditional distribution data logarithm.

*y*=

*Xβ*+

*Zα*+

*ɛ*, in which:

*y*= vector of observations of the studied traits (underlying scales for categorical traits);

**= matrix n×f of incidence (n = total of observations, and f the number of fixed effects of classes), which relates the findings to the systemic effects;**

*X**β*= vector of systemic effects of CG (formed by animals raised on the same farm, born in the same year and season, and evaluated in the same season), YC, AC, and CAT;

**= the matrix n×N of incidence, which lists the observations to genetic additive direct effects, where n is the total number of observations and N number of individuals;**

*Z**α*= vector of random effects representing the direct genetic additive values for each animal (animal model); and

*e*= vector of residual random errors associated to the observations.

*y*) and data (

*β*,

*α*, and ${\sigma}_{e}^{2}$ ), which assumes multivariate normal distribution, is represented as:

*y*|

*β,α*, ${\sigma}_{e}^{2}~N(X\beta +Z\alpha +I{\sigma}_{e}^{2})$ ;

*α*|

*A,*${\sigma}_{a}^{2}~N(0,A{\sigma}_{a}^{2})$ ;

*e*|

*e,*${\sigma}_{e}^{2}~N(0,I{\sigma}_{e}^{2})$ ; thus: ${\sigma}_{a}^{2}$ and ${\sigma}_{e}^{2}$ , components of additive direct genetic and residual (co) variance, respectively;

**, numerators matrix of Wright’s inbreeding coefficient; and**

*A***, identity matrix of equal order to the number of animals with observations.**

*I**U*is a vector of scale base of origin

*r*;

*θ*= (

*b*,

*a*) is the location vector of order parameters

*s*with

*b*(fixed effects in frequentist analysis) and order

*s*with

*a*(random genetic additive direct effect);

**is a matrix incidence of order**

*W**r*by

*s*;

**is an identity matrix of order r by**

*I**r*; and ${\sigma}_{e}^{2}$ is the residual variance.

*y*

*that falls into the category*

_{i}*j*(1, 2, 3, 4, 5: BCS; and 1, 2, 3, 4, 5, 6: MRE) with the given vectors

*β*,

*α*and

*t*(

*t*=

*t*

*,*

_{min}*t*

*, ...,*

_{1}*t*

*,*

_{j-1}*t*

*) and represented as:*

_{máx}*i*animals are defined by

*Ui*, in the underlying scale, and BCS:

*n*is the number of observations for each trait.

*a priori*distribution) for all initial variance, in other words, did not reflect the knowledge about the parameters to be estimated.

*a posteriori*distributions of the deviance of each model, being defined by: DIC =

*D̄*(

*θ*) +

*p*

*; in which:*

_{D}*D̄*(

*θ*) is the global adjustment measure that is the

*posteriori*average of the

*deviance*;

*p*

*is the penalty for complexity of the model (effective number of parameters) given by the difference between the average*

_{D}*posteriori*of the

*deviance*and the

*deviance*of the averages a

*posteriori*of the model parameters of interest. Thus, the smaller the value of DIC the better the fit of the evaluated model [13]. As for FB, the marginal likelihood of a given model M is given by:

*f*(

*y*|

*M*) =

*∫ L*(

*θ*|

*y*)

*π*(

*θ*)

*dθ*

*M*

*and*

_{i}*M*

*), the BF was defined as the reason for the marginal likelihoods of these two models: $F{B}_{i,j}={\scriptstyle \frac{[f({M}_{i}\mid x)/f({M}_{j}\mid x)]}{[f({M}_{i})/f({M}_{j})]}}={\scriptstyle \frac{f(y\mid {M}_{i})}{f(y\mid {M}_{j})}}$ .*

_{j}*FB*

*>1 is the indication that the numerator of the model (*

_{i,j}*M*

*) is the most plausible if*

_{i}*FB*

*<1, the denominator model (*

_{i,j}*M*

*), is preferred, and if*

_{j}*FB*

*= 1, the quality of the two models is the same (*

_{i,j}*M*

*=*

_{i}*M*

*). The threshold model was the FB denominator.*

_{j}*y*|

*β*,

*a*,

*G*

_{0},

*R*

_{0}~

*N*(

*Xβ*+

*Za*,

*R*

_{0}⊗

*I*);

*a*|

*G*

_{0},

*A*~

*N*(0,

*G*

_{0}⊗

*A*);

*e*|

*R*

_{0}~

*N*(0,

*R*

_{0}⊗

*I*), thus:

*A*, additive genetic relationship matrix among animals;

*G*

_{0}, additive genetic (co) variance matrix among traits;

*I*, identity matrix; and

*R*

_{0}, residual (co) variance matrix among traits.

### RESULTS

*a posteriori*distribution parameters, according to [11].

### DISCUSSION

*posteriori*heritability coefficient, it does not change the value of this estimate, considering the second decimal place, as shown in Table 2.

*a posteriori*were heritability valid estimates of categorical traits.

*a posteriori*interval probability [14]. Thus, the threshold model was presented as the greater one with ability to detect the genetic variability in MRE and BCS, when compared to the linear model, according to [3], related to the efficiency of this model for categorical data.

*a posteriori*distribution estimates of the parameters in two-trait analyses.

*longissimus dorsi*. Thus, it is considered that this fact is an explanation for the low heritability estimates for MRE, and then much of the phenotypic variability of the trait is explained by environmental component, so it is important to pay attention to the environmental factors that influence the phenotypic expression of marbling.

*longissimus dorsi*.