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L. R. Schaeffer, April 9, 1999

**Matrix Algebra and Statistics**

- Gelman, A., Carlin, J. B., Stern, H. S., and D. B. Rubin.
1995.
*Bayesian Data Analysis*. Chapman and Hall. - Greene, W. H. 1993.
*Econometric Analysis*. Prentice-Hall, New Jersey. - Harville, D. A. 1997.
*Matrix Algebra From A Statistician's Perspective*. Springer-Verlag New York, Inc. - Searle, S. R. 1982.
*Matrix Algebra Useful for Statistics*. New York:John Wiley. - Sorensen, D. A. 1997. Gibbs Sampling in Quantitative Genetics. Internal Report No. 82, Danish Institute of Animal Science.
- Wackerly, D. D., Mendenhall III, W., and R. L. Scheaffer.
1996.
*Mathematical Statistics with Applications*. Duxbury Press.

**Quantitative Genetics**

- Bulmer, M. G. 1980.
*The Mathematical Theory of Quantitative Genetics*. Oxford University Press. - Falconer, D. S. and T. F. C. Mackay. 1996.
*Introduction to Quantitative Genetics*. Fourth Edition. Longman Group Ltd. - Lynch, M. and B. Walsh. 1998.
*Genetics and Analysis of Quantitative Traits*. Sinauer Associates, Inc.

**Relationships and Inbreeding**

- Chang, H. L., Fernando,R. L., and D. Gianola. 1989. Inverse of an additive additive relationship matrix due to sires and maternal grandsires. J. Dairy Sci. 72:3023-3034.
- Elzo, M. A. 1986. Inverse of single trait additive genetic covariance matrix with unequal variances across additive genetic groups. J. Dairy Sci. 69:569-574.
- Henderson, C. R. 1976. A simple method for computing the inverse of a numerator relationship matrix used for prediction of breeding values. Biometrics 32:69-79.
- Henderson, C. R. 1988. Use of an average numerator relationship matrix for multiple-sire joining. J. Anim. Sci. 66:1614-1621.
- Hoeschele, I. and P. M. Van Raden. 1991. Rapid inversion of dominance relationship matrices for noninbred populations by including sire by dam subclass effects. J. Dairy Sci. 74:557-569.
- Meuwissen, T. H. E. and Z. Luo. 1992. Computing inbreeding coefficients in large populations. Genet. Sel. Evol. 24:305-313.
- Miglior, F. and E. B. Burnside. 1995. Inbreeding of Canadian Holstein cattle. J. Dairy Sci. 78:1163-1167.
- Nejati-Javaremi, A., Smith, C. and J. P. Gibson. 1997. Effect of total allelic relationship on accuracy of evaluation and response to selection. J. Anim. Sci. 75:1738-1745.
- Quaas, R. L. 1976. Computing the diagonal elements and inverse of a large numerator relationship matrix. Biometrics 32:949.
- Quaas, R. L. 1988. Additive genetic model with groups and relationships. J. Dairy Sci. 71:1338-1345.
- Schaeffer, L. R., Kennedy, B. W., and J. P. Gibson. 1989. The inverse of the gametic relationship matrix. J. Dairy Sci. 72:1266-1272.
- Smith, S. P. and A. Maki-Tanila. 1990. Genotypic covariance matrices and their inverses for models allowing dominance and inbreeding. Genet. Sel. Evol. 22:65-91.
- Sorensen, D. A. and B. W. Kennedy. 1983. The use of the relationship matrix to account for genetic drift variance in the analysis of genetic experiments. Theor. Appl. Genet. 66:217.
- Tier, B. 1990. Computing inbreeding coefficients quickly. Genet. Sel. Evol. 22:419-430.
- Van Raden, P. M. and I. Hoeschele. 1991. Rapid inversion of additive by additive relationship matrices by including sire-dam combination effects. J. Dairy Sci. 74:570-579.

**Linear Models**

- Gianola, D. and R. L. Fernando. 1986. Bayesian methods in animal breeding. J. Anim. Sci. 63:217.
- Searle, S. R. 1971.
*Linear Models*. New York, John Wiley.

**Animal Models**

- Gianola, D. and R. L. Fernando. 1986. Bayesian methods in animal breeding theory. J. Anim. Sci. 63:217-244.
- Gianola, D., J. L. Foulley, and R. L. Fernando. 1986. Prediction of breeding values when variances are not known. Genet. Sel. Evol. 18:485-498.
- Henderson, C. R. 1975b. Use of all relatives in intraherd prediction of breeding values and real producing abilities. J. Dairy Sci. 58:1910.
- Henderson, C. R. 1978. Undesirable properties of regressed least squares for prediction of breeding values. J. Dairy Sci. 61:114-120.
- Henderson, C. R. 1984.
*Applications of linear models in animal breeding*. University of Guelph, Guelph, ON. - Kennedy, B. W. and L. R. Schaeffer. 1989. Genetic evaluation under an animal model when identical genotypes are represented in a population. J. Anim. Sci. 67:1946-1955.
- Quaas, R. L. 1988. Additive genetic model with groups and relationships. J. Dairy Sci. 71:1338-1345.
- Quaas, R. L., R. W. Everett, and A. E. McClintock. 1979. Maternal grandsire model for dairy sire evaluation. J. Dairy Sci. 62:1648.
- Quaas, R. L. and E. J. Pollak. 1980. Mixed model methodology for farm and ranch beef cattle testing programs. J. Anim. Sci. 51:1277-1287.
- Quaas, R. L. and E. J. Pollak. 1981. Modified equations for sire models with groups. J. Dairy Sci. 64:1868-1872.
- Robinson, G. K. 1986. Group effects and computing strategies for models for estimating breeding values. J. Dairy Sci. 69:3106-3111.
- Schaeffer, L. R. 1983. Techniques for partitioning sire evaluations. J. Dairy Sci. 66:1519-1527.
- Schaeffer, L. R. and C. R. Henderson. 1983. Best linear unbiased prediction when error vector is correlated with other random vectors in the model. Genet. Sel. Evol. 15:395-400.
- Schaeffer, L. R. and B. W. Kennedy. 1986. Computing strategies for solving mixed model equations. J. Dairy Sci. 69:575-579.
- Schaeffer, L. R. and B. W. Kennedy. 1989. Effects of embryo transfer in beef cattle on genetic evaluation methodology. J. Anim. Sci. 67:2536-2543.
- Simianer, H. 1991. Prospects for third generation
methods of genetic evaluation. 42
^{nd}Annual Meeting of the European Association for Animal Production, Berlin. - Sorensen, D. A. and B. W. Kennedy. 1984. Estimation of response to selection using least-squares and mixed model methodology. J. Anim. Sci. 58:1097-1106.
- Sorensen, D. A. and B. W. Kennedy. 1986. Analysis of selection experiments using mixed model methodology. J. Anim. Sci. 63:245-258.

**Variance Components**

- Boichard, D., L. R. Schaeffer, and A. J. Lee. 1992. Approximate restricted maximum likelihood and approximate prediction error variance of the Mendelian sampling effect. Genet. Sel. Evol. 24:331-343.
- Casella, G. and E. I. George. 1992. Explaining the Gibbs sampler. The American Statistician 46(3):167-174.
- Corbeil, R. R. and S. R. Searle. 1976. A comparison of variance component estimators. Biometrics 32:779-791.
- Da, Y., M. Grossman, and I. Misztal. 1989. Prediction error variance and REML estimation for animal model with relationship grouping. J. Dairy Sci. 72:2125-2135.
- Dempfle, L., C. Hagger, and M. Schneeberger. 1983. On the estimation of genetic parameters via variance components. Genet. Sel. Evol. 15:425-444.
- Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. J. Royal Stat. Soc., Ser B 39:1-38.
- Gelfand, A. E., S. I. Hills, A. Racine-Poon and A. F. M. Smith. 1990. Illustration of Bayesian inference in normal data models using Gibbs sampling. J. Amer. Stat. Assoc. 90:972-985.
- Gianola, D. and J.-L. Foulley. 1990. Variance estimation from integrated likelihoods (VEIL). Genet. Sel. Evol. 22:403-418.
- Gianola, D. and R. L. Fernando. 1986. Bayesian methods in animal breeding. J. Anim. Sci. 63:217.
- Graser, H.-U., S. P. Smith, and B. Tier. 1987. A derivative free approach for estimating variance components in animal models by restricted maximum likelihood. J. Anim. Sci. 64:1362-1370.
- Hartley, H. O. and J. N. K. Rao. 1967. Maximum likelihood estimation for the mixed analysis of variance model. Biometrika 54:93-108.
- Hartley, H. O., J. N. K. Rao, and L. R. LaMotte. 1978. A simple synthesis based method of variance component estimation. Biometrics 34:233-242.
- Harville, D. A. 1974. Bayesian inference for variance components using only error contrasts. Biometrika 61:383-385.
- Harville, D. A. 1977. Maximum-likelihood approaches to variance component estimation and to related problems. J. Am. Statist. Assoc. 72:320-340.
- Henderson, C. R. 1953. Estimation of variance and covariance components. Biometrics 9:226-310.
- Henderson, C. R. 1978. Simulation to examine distributions of estimators of variances and ratios of variances. J. Dairy Sci. 61:267-273.
- Henderson, C. R. 1980. A simple method of unbiased estimation of variance components in the mixed model. Abstract of 72nd Annual Meeting of American Society of Animal Science, Ithaca, New York.
- Henderson, C. R. 1984.
*Applications of linear models in animal breeding*. University of Guelph, Guelph, ON. - Henderson, C. R. 1986. Estimation of singular covariance matrices of random effects. J. Dairy Sci. 69:2379-2385.
- Henderson, C. R., S. R. Searle, and L. R. Schaeffer. 1974. Invariance and calculation of Method 2 of estimating variance components. Biometrics 30:583-588.
- Hudson, G. F. S. and L. D. Van Vleck. 1982. Estimation of components of variance by Method 3 and Henderson's new method. J. Dairy Sci. 65:435-441.
- Jensen, J., C. S. Wang, D. A. Sorensen, and D. Gianola. 1994(?). Bayesian inference on variance and covariance components for traits influenced by maternal and direct genetic effects, using the Gibbs sampler. Acta. Scand. (??).
- Johnson, D. L. and R. Thompson. 1995. Restricted maximum likelihood estimation of variance components for univariate animal models using sparse matrix techniques and average information. J. Dairy Sci. 78:449-456.
- LaMotte, L. R. 1970. A class of estimators of variance components. Technical Report 10, Dept. of Stat., Univ. of Kentucky, Lexington.
- LaMotte, L. R. 1971. Locally best quadratic estimators of variance components. Technical Report 22, Dept. of Stat., Univ. of Kentucky, Lexington.
- Meyer, K. 1986. Between algorithms: A "short cut" restricted maximum likelihood procedure to estimate variance components. J. Dairy Sci. 69:1904-1916.
- Meyer, K., and S. P. Smith. 1996. Restricted maximum likelihood estimation for animal models using derivatives of the likelihood. Genet. Sel. Evol. 28:23-49.
- Misztal, I. 1994. Comparison of computing properties of derivative and derivative free algorithms in variance-component estimation by REML. J. Anim. Breed. Genet. 111:346-355.
- Ouweltjes, W., L. R. Schaeffer, and B. W. Kennedy. 1988. Sensitivity of methods of variance component estimation to culling type of selection. J. Dairy Sci. 71:773-779.
- Patterson, H. D. and R. Thompson. 1971. Recovery of interblock information when block sizes are unequal. Biometrika 58:545-554.
- Rao, C. R. 1970. Estimation of heteroscedastic variances in linear models. J. Am. Statist. Assoc. 65:161-172.
- Rao, C. R. 1971. Estimation of variance covariance components - MINQUE theory. J. Mult. Anal. 1:445-456.
- Rodda, D. D., L. R. Schaeffer, K. Mullen, and G. W. Friars. 1977. Measuring the precision of genetic parameters by a simulation technique. Theor. Appl. Genet. 51:35-39.
- Schaeffer, L. R. 1975. Disconnectedness and variance component estimation. Biometrics 31:969-977.
- Schaeffer, L. R. 1976. Maximum likelihood estimation of variance components in dairy cattle breeding research. J. Dairy Sci. 59:2146-2151.
- Schaeffer, L. R. 1986. Estimation of variances and covariances within the allowable parameter space. J. Dairy Sci. 69:187-194.
- Schaeffer, L. R. 1986. Pseudo expectation approach to variance component estimation. J. Dairy Sci. 69:2884-2889.
- Schaeffer, L. R. 1987. Estimation of variance components under a selection model. J. Dairy Sci. 70:661-671.
- Schaeffer, L. R. 1987. Improving the convergence rates of iterative methods of variance component estimation. J. Dairy Sci. 70:331-336.
- Schaeffer, L. R., Wilton, J. W., and R. Thompson. 1978. Simultaneous estimation of variance and covariance components from multitrait mixed model equations. Biometrics 34:199-208.
- Searle, S. R. 1979. Notes on Variance Component Estimation: A Detailed Account of Maximum Likelihood and Kindred Methodology. Biometrics Unit, Warren Hall, Cornell University, Ithaca, NY.
- Searle, S. R. 1989. Variance components - some history and a summary account of estimation methods. J. Anim. Breed. Genet. 106:1-29.
- Searle, S. R. and T. R. Rounsaville. 1974. A note on estimating covariance components. The Amer. Stat. 28:67-68.
- Searle, S. R., G. Casella, and C. E. McCulloch. 1992.
*Variance Components*. John Wiley & Sons, New York. - Simianer, H. 1988. Efficient search strategies in iterative algorithms for variance component estimation. J. Anim. Breed. Genet. 105:468-483.
- Smith, S. P. and H. U. Graser. 1986. Estimating variance components in a class of models by restricted maximum likelihood. J. Dairy Sci. 69:1156-1165.
- Sorensen, D. A. and B. W. Kennedy. 1984. Estimation of genetic variances from unselected and selected populations. J. Anim. Sci. 59:1213-1223.
- Southwood, O. I., Kennedy, B. W., Meyer, K. and J. P. Gibson. 1989. Estimation of additive maternal and cytoplasmic genetic variances in animal models. J. Dairy Sci. 72:3006-3012.
- Thompson, E. A. and R. G. Shaw. 1990. Pedigree analysis for quantitative traits: variance components without matrix inversion. Biometrics 46:399-413.
- Thompson, R. and K. Meyer. 1990. Estimating genetic parameters using an animal model with imaginary effects. Genet. Sel. Evol. 22:133-147.
- Van Raden, P. M. and Y. C. Jung. 1988. A general purpose approximation to restricted maximum likelihood: the tilde-hat approach. J. Dairy Sci. 71:187-194.
- Van Tassell, C. P. 1994. The use of Gibbs sampling for variance component estimation with simulated and weaning weight data using animal and maternal effects models. Ph.D. Thesis. Cornell University, Ithaca, New York.
- Wang, C.S., J. J. Rutledge, and D. Gianola. 1993. Marginal inferences about variance components in a mixed linear model using Gibbs sampling. Genet. Sel. Evol. 25:41-62.
- Xu, S., W. R. Atchley, and W. M. Muir. 1994. Partial and conditional maximum likelihood for variance-component estimation. J. Anim. Breed. Genet. 111:178-188.
- Xu, S. and W. R. Atchley. 1996. A Monte-Carlo algorithm for maximum likelihood estimation of variance components. Genet. Sel. Evol. 28:329-343.

**Maternal Effects Model**

- Cue, R. I. and J. F. Hayes. 1985. Correlations of various direct and maternal effects for calving ease. J. Dairy Sci. 68:374-381.
- Schaeffer, L. R. and B. W. Kennedy. 1989. Effects of embryo transfer in beef cattle on genetic evaluation methodology. J. Anim. Sci. 67:2536-2543.
- Thompson, R. 1976. The estimation of maternal genetic variances. Biometrics 32:903-918.

**Covariance Functions, Random Regressions**

- Anderson, S. and B. Pedersen. 1996. Growth and food intake curves for group-housed gilts and castrated male pigs. Anim. Sci. 63:457.
- Diggle, P. J., K.-Y. Liang, and S. L. Zeger. 1994.
*Analysis of Longitudinal Data*. Clarendon Press, Oxford. - Henderson, C. R., Jr. 1982. Analysis of covariance in the mixed model: higher-level, nonhomogeneous, and random regressions. Biometrics 38:623.
- Kirkpatrick, M. and N. Heckman. 1989. A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters. J. Math. Biol. 27:429-450.
- Kirkpatrick, M., D. Lofsvold, and M. Bulmer. 1990. Analysis of the inheritance, selection and evolution of growth trajectories. Genetics 124:979-993.
- Kirkpatrick, M. and D. Lofsvold. 1992. Measuring selection and constraint in the evolution of growth. Evolution 46:954-971.
- Kirkpatrick, M., W. G. Hill, and R. Thompson. 1994. Estimating the covariance structure of traits during growth and ageing, illustrated with lactating dairy cattle. Genet. Res. 64:57-69.
- Meyer, K. 1997. An 'average information' restricted maximum likelihood algorithm for estimating reduced rank genetic covariance matrices of covariance functions for animal models with equal design matrices. Genet. Sel. Evol. 29:97-116.
- Meyer, K. and W. G. Hill. 1997. Estimation of genetic and phenotypic covariance functions for longitudinal or 'repeated' records by restricted maximum likelihood. Livest. Prod. Sci. 47:185.
- Schaeffer, L. R., and J.C.M. Dekkers. 1994. Random regressions in animal models for test-day production in dairy cattle. Proc. 5th World Congr. Genet. Appl. Livest. Prod., Guelph, 18:443.
- van der Werf, J. and L. R. Schaeffer. 1997. Random regression in animal breeding. Course Notes, CGIL June 25-28, 1997.

**Multiple Traits**

- Henderson, C. R. 1984. Estimation of variances and covariances under multiple trait models. J. Dairy Sci. 67:1581-1589.
- Henderson, C. R. and R. L. Quaas. 1976. Multiple trait evaluation using relatives' records. J. Anim. Sci. 43:1188-1197.
- Pollak, E. J. and R. L. Quaas. 1981. Monte Carlo study of within-herd multiple trait evaluation of beef cattle growth traits. J. Anim. Sci. 52:248-256.
- Schaeffer, L. R. 1984. Sire and cow evaluation under multiple trait models. J. Dairy Sci. 67:1567-1580.
- Schaeffer, L. R., J. W. Wilton, and R. Thompson. 1978. Simultaneous estimation of variance and covariance components from multitrait mixed model equations. Biometrics 34:199-208.

**Non-Additive Genetic Models**

- Henderson, C. R. 1985. Best linear unbiased prediction of nonadditive genetic merits in noninbred populations. J. Anim. Sci. 60:111-117.
- Henderson, C. R. 1985. MIVQUE and REML estimation of additive and nonadditive genetic variances. J. Anim. Sci. 61:113-121.
- Henderson, C. R. 1989. Prediction of merits of potential matings from sire-maternal grandsire models with non additive genetic effects. J. Dairy Sci. 72:2592-2605.
- Hoeschele, I. and A. R. Vollema. 1992. Estimation of variance components with dominance and inbreeding in dairy cattle. J. Anim. Breed. Genet.
- Johansson, K., Kennedy, B. W. and M. Quinton. 1993. Prediction of breeding values and dominance effects from mixed models with approximations of the dominance relationship matrix. Livest. Prod. Sci. 34:213-223.
- Miglior, F., Burnside, E. B., and B. W. Kennedy. 1995. Production traits of Holstein cattle: Estimation of nonadditive genetic variance components and inbreeding depression. J. Dairy Sci. 78:1174-1180.
- van der Werf, J. H. J. and W. de Boer. 1989. Influence of non additive effects on estimation of genetic parameters in dairy cattle. J. Dairy Sci. 72:2606-2614.

**Effects of Selection**

- Belonsky, G. M. and B. W. Kennedy. 1988. Selection on individual phenotype and best linear unbiased predictor of breeding value in a closed swine herd. J. Anim. Sci. 66:1124-1131.
- Blair, H. T. and E. J. Pollak. 1984. Estimation of genetic trend in a selected population with and without the use of a control population. J. Anim. Sci. 58:878-886.
- Ducrocq, V. and R. L. Quaas. 1988. Prediction of genetic response to truncation selection across generations. J. Dairy Sci. 71:2543-2553.
- Fries, L. A. and F. S. Schenkel. 1993. Estimation and
prediction under a selection model. Presented at 30
^{th}Reuniao Anual da Sociedade Brasileira de Zootecnia, Rio de Janeiro. - Gianola, D., S. Im, and R. L. Fernando. 1988. Prediction of breeding value under Henderson's selection model: A Revisitation. J. Dairy Sci. 71:2790-2798.
- Goffinet, B. 1983. Selection on selected records. Genet. Sel. Evol. 15:91-98.
- Henderson, C. R. 1975a. Best linear unbiased estimation and prediction under a selection model. Biometrics 31:423-448.
- Henderson, C. R. 1988. A simple method to account for selected base populations. J. Dairy Sci. 71:3399-3404.
- Hudson, G. F. S. and L. R. Schaeffer. 1984. Monte Carlo comparison of sire evaluation models in populations subject to selection and non-random mating. J. Dairy Sci. 67:1264-1272.
- Pollak, E. J. and R. L. Quaas. 1981. Monte Carlo study of genetic evaluations using sequentially selected records. J. Anim. Sci. 52:257-264.
- Pollak, E. J., van der Werf, J., and R. L. Quaas. 1984. Selection bias and multiple trait evaluation. J. Dairy Sci. 67:1590-1596.
- Schenkel, F. S. 1998. Studies on effects of parental selection on estimation of genetic parameters and breeding values of metric traits. Ph.D. Thesis. University of Guelph. Guelph, Ontario, Canada.
- Sorensen, D. A., Wang, C. S., Jensen, J., and D. Gianola. 1994. Bayesian analysis of genetic change due to selection using Gibbs sampling. Genet. Sel. Evol. 26:333-360.
- Van Vleck, L. D. 1968. Selection bias in estimation of the genetic correlation. Biometrics 24:951-962.

**Reduced Animal Models**

- Blair, H. T. and E. J. Pollak. 1984. Comparison of an animal model and an equivalent reduced animal model for computational efficiency using mixed model methodology. J. Anim. Sci. 58:1090-1096.
- Henderson, C. R. 1986. Estimation of variances in animal model and reduced animal model for single traits and single records. J. Dairy Sci. 69:1394-1402.
- Quaas, R. L. and E. J. Pollak. 1980. Mixed model methodology for farm and ranch beef cattle testing programs. J. Anim. Sci. 51:1277-1287.

**Connectedness**

- Fernando, R. L., D. Gianola, and M. Grossman. 1983. Identifying all connected subsets in a two-way classification without interaction. J. Dairy Sci. 66:1399-1402.
- Kennedy, B. W. and D. Trus. 1993. Considerations on genetic connectedness between management units under an animal model. J. Anim. Sci. 71:2341-2352.
- Schaeffer, L. R. 1975. Disconnectedness and variance component estimation. Biometrics 31:969-977.
- Schmitz, F., Everett, R. W., and R. L. Quaas. 1991. Herd-year-season clustering. J. Dairy Sci. 74:629-636.
- Visscher, P. M. and M. E. Goddard. 1993. Fixed and random contemporary groups. J. Dairy Sci. 76:1444-1454.
- Weeks, D. L. and D. R. Williams. 1964. A note on the determination of connectedness in an N-way cross classification. Technometrics 6:319-324.

**Heterogeneity of Variances**

- Brotherstone, S. and W. G. Hill. 1986. Heterogeneity of variance amongst herds for milk production. Anim. Prod. 42:297-303.
- Famula, T. R. 1989. Detection of heterogeneous variance in herd production groups. J. Dairy Sci. 72:715-721.
- Foulley, J. L., Gianola, D., San Cristobal, M., and S. Im. 1990. A method for assessing extent and sources of heterogeneity of residual variances in mixed linear models. J. Dairy Sci. 73:1612-1624.
- Meuwissen, T. H. E., De Jong, G., and B. Engel. 1996. Joint estimation of breeding values and heterogeneous variances of large data files. J. Dairy Sci. 79:310-316.
- Weigel, K. A. and D. Gianola. 1993. A computationally simple Bayesian method for estimation of heterogeneous within herd phenotypic variances. J. Dairy Sci. 76:1455-1465.

**Threshold Models**

- Foulley, J. L. and D. Gianola. 1984. Estimation of genetic merit from bivariate all or none responses. Genet. Sel. Evol. 16:285-306.
- Foulley, J. L. and D. Gianola. 1986. Sire evaluation for multiple binary responses when information is missing on some traits. J. Dairy Sci. 69:2681-2695.
- Gianola, D. 1982. Theory and analysis of threshold characters. J. Anim. Sci. 54:1079-1096.
- Harville, D. A. and R. W. Mee. 1984. A mixed model procedure for analyzing ordered categorical data. Biometrics 40:393-408.
- Snell, E. J. 1964. A scaling procedure for ordered categorical data. Biometrics 20:592.

**Computing Strategies**

- Garcia-Cortes, L. A., Moreno, C., Varona, L., and J. Altarriba. 1995. Estimation of prediction error variances by resampling. J. Anim. Breed. Genet. 112:176-182.
- Graser, H. U. and B. Tier. 1997. Applying the concept of number of effective progeny to approximate accuracies of predictions derived from multiple trait analyses. Presented at Australian Association of Animal Breeding and Genetics.
- Henderson, C. R. 1978. Simulation to examine distributions of estimators of variances and ratios of variances. J. Dairy Sci. 61:267-273.
- Henderson, C. R. 1985. Equivalent linear models to reduce computations. J. Dairy Sci. 68:2267-2277.
- Hudson, G. F. S. 1984. Extension of a reduced animal model to recursive prediction of breeding values. J. Anim. Sci. 59:1164-1175.
- Meyer, K. 1989. Approximate accuracy of genetic evaluation under an animal model. Livest. Prod. Sci. 21:87-100.
- Misztal, I. and D. Gianola. 1987. Indirect solution of mixed model equations. J. Dairy Sci. 70:716-723.
- Misztal, I., Gianola, D., and J. L. Foulley. 1989. Computing aspects of a nonlinear method of sire evaluation for categorical data. J. Dairy Sci. 72:1557-1568.
- Misztal, I. and M. Perez-Enciso. 1993. Sparse matrix inversion for restricted maximum likelihood estimation of variance components by expectation-maximization. J. Dairy Sci. 76:1479-1483.
- Schaeffer, L. R. and B. W. Kennedy. 1986. Computing strategies for solving mixed model equations. J. Dairy Sci. 69:575-579.
- Van Vleck, L. D. and D. J. Dwyer. 1985. Successive overrelaxation, block iteration, and method of conjugate gradients for solving equations for multiple trait evaluation of sires. J. Dairy Sci. 68:760-767.
- Van Vleck, L. D. and D. J. Dwyer. 1985. Comparison of iterative procedures for solving equations for sire evaluation. J. Dairy Sci. 68:1006-1014.

**Test Day Analyses in Dairy Cattle**

- Ali, T. E., and L. R. Schaeffer. 1987. Accounting for covariances among test day milk yields in dairy cows. Can. J. Anim. Sci. 67:637.
- Danell, B. 1982. Studies on lactation yield and individual test-day yields of Swedish dairy cows. I. Environmental influence and development of adjustment factors. Acta. Agric. Scand. 32: 65.
- Danell, B. 1982. Studies on lactation yield and individual test-day yields of Swedish dairy cows. II. Estimates of genetic and phenotypic parameters. Acta. Agric. Scand. 32:82.
- Guo, Z., and H. H. Swalve. 1995. Modelling of the lactation curve as a sub-model in the evaluation of test day records. INTERBULL Mtg., Prague, Sept. 7-8. INTERBULL Bulletin No. 11., Int. Bull Eval. Service, Uppsala, Sweden.
- Jamrozik, J., and L. R. Schaeffer. 1997. Estimates of genetic parameters for a test day model with random regressions for production of first lactation Holsteins. J. Dairy Sci. 80:762-770.
- Jamrozik, J., L. R. Schaeffer, and J.C.M. Dekkers. 1997. Genetic evaluation of dairy cattle using test day yields and random regression model. J. Dairy Sci. 80:1217-1226.
- Jamrozik, J., G. J. Kistemaker, J. C. M. Dekkers, and L. R. Schaeffer. 1997. Comparison of possible covariates for use in a random regression model for analyses of test day yields. J. Dairy Sci. 80:2550-2556.
- Jamrozik, J., L. R. Schaeffer, and F. Grignola. 1998. Genetic parameters for production traits and somatic cell score of Canadian Holsteins with multiple trait random regression model. 6WCGALP. 23:303-306.
- Kettunen, A., E. A. Mantysaari, I. Stranden, J. Poso, and M. Lidauer. 1998. Estimation of genetic parameters for first lactation test day milk production using random regression models. 6WCGALP. 23:307-310.
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