Resumo: O objetivo deste estudo foi investigar a existência de variabilidade genética aditiva sobre a variância residual do ganho de peso do nascimento à desmama (GND) de bovinos Nelore e as perspectivas de se explorar diferenças entre genótipos para variância residual para a obtenção de maior uniformidade de produção, por meio de seleção. Diferentes abordagens, implementadas em dois passos, foram estudadas: Inicialmente, avaliaram-se três modelos para análise de medidas de dispersão dos resíduos associados às observações de GND da progênie de touros Nelore. O modelo considerado mais promissor foi empregado em estudo subsequente, em que foi investigado o impacto do tamanho de progênie dos touros nas estimativas obtidas para variância aditiva sobre a dispersão residual e estimadores de dispersão em diferentes escalas foram comparados. A confiabilidade de tal abordagem foi verificada por meio de simulação de Monte Carlo. Um último estudo avaliou a possibilidade de se considerarem, simultaneamente, efeitos aditivos e ambientais sobre a variância residual de GND, empregando-se diferentes modelos para análise do logaritmo natural do quadrado do resíduo associado a cada observação. Concluiu-se que, ao se considerar famílias de grande tamanho, seria possível obter predições acuradas do mérito genético dos touros para a variância residual e alguma resposta em termos de uniformidade de produção, sendo a abordagem do último estudo considerada a mais adequada para este fim. Desconsiderar efeitos ambientais sobre a variância residual no segundo passo das análises pode levar a superestimação da variância aditiva sobre a dispersão residual, bem como da resposta esperada à seleção / Abstract: This study was carried out to investigate the existence of genetic variability on residual variance of beef cattle production traits and to evaluate the opportunity for improvement in uniformity of such traits by selecting for lower residual variance. Different two-step approaches were studied to address these questions: Firstly, three models were employed to analyze different measures associated with residual dispersion of weight gain from birth to weaning (GND) in the progeny of Nellore sires. The model that performed best was employed in a subsequent study to access the impact of progeny size on estimates of additive variance for residual dispersion, also aiming to compare dispersion estimators of different scales and to predict selection response in each situation. Reliability of this approach was verified by Monte Carlo simulation. The possibility of considering, simultaneously, additive and environmental effects on residual variance of GND was investigated by analyzing log squared residuals associated with each observation according to different models. It was concluded that, by considering large sire families, accurate estimates of genetic merit of sires for residual variance could be obtained as well as some improvement in uniformity of GND. Analyzing log squared residuals associated with each observation was considered the most promising approach for this task. Ignoring environmental effects at the level of residual variance could lead to inflated estimates of additive variance of residual dispersion, therefore implying in overestimation of response to selection / Orientador: Sandra Aidar de Queiroz / Coorientador: Roberto Carvalheiro / Banca: Vanerlei Mozaquatro Roso / Banca: Henrique Nunes de Oliveira / Mestre

Made available in DSpace on 2014-06-11T19:26:06Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-02-01Bitstream added on 2014-06-13T18:54:02Z : No. of bitstreams: 1 neves_hhr_me_jabo.pdf: 1347813 bytes, checksum: 533a7d64f9bb2ee7d83391c75514635d (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / O objetivo deste estudo foi investigar a existência de variabilidade genética aditiva sobre a variância residual do ganho de peso do nascimento à desmama (GND) de bovinos Nelore e as perspectivas de se explorar diferenças entre genótipos para variância residual para a obtenção de maior uniformidade de produção, por meio de seleção. Diferentes abordagens, implementadas em dois passos, foram estudadas: Inicialmente, avaliaram-se três modelos para análise de medidas de dispersão dos resíduos associados às observações de GND da progênie de touros Nelore. O modelo considerado mais promissor foi empregado em estudo subsequente, em que foi investigado o impacto do tamanho de progênie dos touros nas estimativas obtidas para variância aditiva sobre a dispersão residual e estimadores de dispersão em diferentes escalas foram comparados. A confiabilidade de tal abordagem foi verificada por meio de simulação de Monte Carlo. Um último estudo avaliou a possibilidade de se considerarem, simultaneamente, efeitos aditivos e ambientais sobre a variância residual de GND, empregando-se diferentes modelos para análise do logaritmo natural do quadrado do resíduo associado a cada observação. Concluiu-se que, ao se considerar famílias de grande tamanho, seria possível obter predições acuradas do mérito genético dos touros para a variância residual e alguma resposta em termos de uniformidade de produção, sendo a abordagem do último estudo considerada a mais adequada para este fim. Desconsiderar efeitos ambientais sobre a variância residual no segundo passo das análises pode levar a superestimação da variância aditiva sobre a dispersão residual, bem como da resposta esperada à seleção / This study was carried out to investigate the existence of genetic variability on residual variance of beef cattle production traits and to evaluate the opportunity for improvement in uniformity of such traits by selecting for lower residual variance. Different two-step approaches were studied to address these questions: Firstly, three models were employed to analyze different measures associated with residual dispersion of weight gain from birth to weaning (GND) in the progeny of Nellore sires. The model that performed best was employed in a subsequent study to access the impact of progeny size on estimates of additive variance for residual dispersion, also aiming to compare dispersion estimators of different scales and to predict selection response in each situation. Reliability of this approach was verified by Monte Carlo simulation. The possibility of considering, simultaneously, additive and environmental effects on residual variance of GND was investigated by analyzing log squared residuals associated with each observation according to different models. It was concluded that, by considering large sire families, accurate estimates of genetic merit of sires for residual variance could be obtained as well as some improvement in uniformity of GND. Analyzing log squared residuals associated with each observation was considered the most promising approach for this task. Ignoring environmental effects at the level of residual variance could lead to inflated estimates of additive variance of residual dispersion, therefore implying in overestimation of response to selection

Beef cattle are continuously selected for different traits and the success in improving these traits has been remarkable. However, for certain traits, it is essential not only to improve the average performance, but also to control the variation around the mean. There is evidence that residual variance may be under genetic control, which opens the possibility of selecting for uniformity. In this sense, the objectives of the present dissertation were: 1) to investigate the extent of genetic heterogeneity of residual variance at the pedigree level in birth weight (BW), weaning weight (WW), yearling weight (YW), foot angle (FA), and claw set (CS) in American Angus cattle; 2) to compare the results of different genetic heterogeneity models; 3) to evaluate the effectiveness of Box-Cox transformation in continuous traits; and 4) to address limitations and explore alternative solutions for implementing genetic parameters for residual variance in genetic evaluations. The first study investigated the genetic heterogeneity of residual variances for BW, WW, and YW. Three models were compared: a homoscedastic residual variance model (M1), a double hierarchical generalized linear model (DHGLM, M2), and a genetically structured environmental variance model (MCMC, M3). The results showed significant genetic heterogeneity of residual variances in growth traits, suggesting the possibility of selection for uniformity. The genetic coefficient of variation for residual variance ranged from 0.90 to 0.92 in M2 and 0.31 to 0.38 in M3 for BW, 0.64 in M2 and 0.01 to 0.29 in M3 for WW, and 0.67 to 0.63 in M2 and 0.25 to 0.31 in M3 for YW. Low heritability estimates for residual variance were found, particularly in M2 (0.08 for BW, 0.06 for WW, and 0.09 for YW). The study identified both negative and positive genetic correlations between mean and residual variance, depending on the trait and data transformation. Negative correlations suggest the potential to increase trait means while decreasing residual variance. However, positive correlations indicate that the genetic response to selection for uniformity may be limited unless a selection index is used. Data transformation reduced skewness but did not eliminate genetic heterogeneity of residual variances. The Bayesian approach provided higher estimates of additive genetic variance for residual variance compared to DHGLM. Overall, the findings indicate the potential to reduce variability through selection and lay the groundwork for incorporating uniformity of growth traits into breeding goals. The second study focused on the genetic heterogeneity of residual variance for two foot conformation traits, FA and CS. Using 45,667 phenotypic records collected between 2009 and 2021, three models were compared: a traditional homoscedastic residual variance model (M1), a DHGLM (M2), and a genetically structured environmental variance model (M3). Results showed that heritability estimates for FA and CS means were within expected ranges, although lower in M2. Despite low heritability estimates for residual variance (0.07 for FA and 0.05 for CS in M2), significant genetic coefficients of variation were found, suggesting that selection on trait mean would also influence residual variance. Positive genetic correlations between mean and residual variance in M2 and M3 indicate that selection for uniformity is feasible, but may require additional strategies such as selection indices. The study highlights the potential of FA and CS as indicators for breeding programs aimed at improving production uniformity in beef cattle. Our findings suggest that selection for uniformity in growth and foot score traits in beef cattle may be limited by low heritability of residual variance and moderate to high positive genetic correlations between mean and residual variance. This was observed for most of the traits studied. To overcome these challenges, further research is needed, particularly to explore genomic information to improve the prediction accuracy of estimated breeding values (EBV) for residual variance. Although studies of uniformity using genomic data are limited, they have shown improved EBV accuracy for residual variance. Additionally, alternative methods for measuring uniformity, such as different uniformity or resilience indicators, should be considered, especially with advances in digital phenotyping. Precision livestock farming technologies that allow for extensive data collection on various production traits should be integrated into the development of new uniformity indicators. This dissertation provides valuable insights into the genetic heterogeneity of residual variance in American Angus cattle and highlights the complexity of selecting for uniformity while improving mean traits. Continued research with larger data sets, genomic information, and further methodological refinement will be critical to advance these findings to improve uniformity and productivity in beef cattle breeding. / Doctor of Philosophy / Uniformity in livestock breeding refers to the goal of reducing variability in certain traits within a livestock population to achieve more consistent and predictable outcomes. This is particularly important for traits that affect productivity, economic efficiency, animal welfare, and product quality. By achieving greater uniformity, producers can optimize management practices, improve marketability, and enhance the overall efficiency of animal production systems. Residual variance refers to the variation in traits that is not explained by known genetic or environmental factors. Recent research suggests that residual variance may be under genetic control, meaning that it is possible to select animals that not only have desirable traits, but also have less variability in those traits. Therefore, this dissertation investigates the genetic control of residual variance that may allow selection for uniformity in traits. The research focused on American Angus cattle and aimed to 1) investigate genetic heterogeneity of residual variance in traits, such as birth weight, weaning weight, yearling weight, foot angle, and claw set; 2) compare different genetic models; 3) evaluate the effectiveness of data transformations; and 4) address limitations in genetic evaluations. The first study examined genetic heterogeneity in growth traits using three models. It revealed significant genetic variability, suggesting the potential for selection for uniformity. The study found both positive and negative genetic correlations between trait means and residual variance, indicating varying potential for reducing variance while improving trait means. Data transformations reduced skewness but did not eliminate genetic heterogeneity. A Bayesian approach provided higher estimates of genetic variance than other methods. The second study focused on foot conformation traits with over 45,000 records. The study showed that despite low heritability for residual variance, there was significant genetic variation, indicating the possibility of altering residual variance through selection. Positive genetic correlations suggested that additional strategies, such as selection indices, may be needed to achieve uniformity in practice. Overall, the findings highlight the complexity of selecting for uniformity while improving average traits and underscore the need for further research, particularly using genomic data, to improve prediction accuracy. Integrating precision livestock farming technologies could help develop new indicators of uniformity, improving productivity and uniformity in beef cattle breeding.

Linha de pesquisa: Melhoramento animal. / Submitted by Jos? Henrique Henrique (jose.neves@ufvjm.edu.br) on 2017-09-29T00:35:26Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) diego_coimbra_alcantara.pdf: 1887370 bytes, checksum: 3b18dc6adcb9630901b41a57c4a4a351 (MD5) / Approved for entry into archive by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2017-10-09T14:23:40Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) diego_coimbra_alcantara.pdf: 1887370 bytes, checksum: 3b18dc6adcb9630901b41a57c4a4a351 (MD5) / Made available in DSpace on 2017-10-09T14:23:40Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) diego_coimbra_alcantara.pdf: 1887370 bytes, checksum: 3b18dc6adcb9630901b41a57c4a4a351 (MD5) Previous issue date: 2016 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico (CNPq) / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Funda??o de Amparo ? Pesquisa do estado de Minas Gerais (FAPEMIG) / Objetivou-se com este estudo, caracterizar a intera??o gen?tipo x ambiente em codornas de corte, alimentadas com dietas contendo diferentes rela??es de triptofano:lisina, via normas de rea??o. Para realizar o experimento foram utilizadas duas linhagens de codornas de corte, LF1 e LF2. A ra??o fornecida no per?odo de crescimento, nascimento aos 21 dias de idade, continha uma rela??o de 0,20% de triptofano:lisina, e no per?odo final do crescimento, 22 a 35 dias, as codornas foram separadas em 5 tratamentos com as rela??es: 0,15; 0,20; 0,25; 0,30; 0,35% de triptofano:lisina. As aves foram pesadas aos 28 e 35 dias e abatidas aos 35 dias de idade. As caracter?sticas avaliadas foram os pesos pr?-abate, peso 28, peso 35, peso e rendimentos da carca?a, peito, coxa+sobrecoxa e as caracter?sticas de qualidade da carne. As an?lises foram realizadas utilizando modelos de regress?o aleat?ria considerando efeito fixo de sexo e o efeito aleat?rio gen?tico aditivo direto como fun??es das rela??es triptofano:lisina da dieta, admitindo-se homogeneidade de vari?ncia residual. Os resultados para desempenho, caracter?sticas de carca?a e caracter?sticas de qualidade da carne indicam que o coeficiente de regress?o do intercepto (b0), foi maior que o coeficiente de regress?o aleat?rio (b1). A herdabilidade e a vari?ncia gen?tica aditiva foram influenciadas pelas diferentes rela??es triptofano:lisina da dieta. Houve intera??o gen?tipo x ambiente para as caracter?sticas rendimento de carca?a, rendimento de peito e rendimento de coxa+sobrecoxa. As caracter?sticas de qualidade da carne CRA, b*, c* e H* (LF1) e CRA, PPC, L* e H* (LF2) apresentaram intera??o gen?tipo x ambiente. A intera??o gen?tipo x ambiente observada para as caracteristicas de rendimento e qualidade da carne indicam que a sele??o seja feita na rela??o triptofano:lisina em que as codornas ser?o criadas. / Disserta??o (Mestrado) ? Programa de P?s-Gradua??o em Zootecnia, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2016. / We animed of this experiment was to characterize the genotype x environment interaction in the production of meat quails, fed diets containing different tryptophan:lysine ratios, via reaction standards. Two lines of cutting quails, LF1 and LF2, were used to perform the experiment. The feed provided in the growing period, from birth to 21 days, contained a 0.20% tryptophan:lysine ratio and in the final growth period, from 22 to 35 days of age, quails were separated into 5 treatments containing the Ratios of 0.15; 0.20; 0.25; 0.30; 0.35% tryptophan: lysine. The birds were weighed at 28 and 35 days of age and slaughtered at 35 days of age. The evaluated characteristics were the pre-slaughter weights, weight 28, weight 35, weight and yields of the carcass, breast, thigh + sobrecoxa and the quality traitsof the meat. The analyzes were performed using random regression models considering fixed sex effect and direct additive genetic random effect as functions of the tryptophan:lysine ratios of the diet, assuming homogeneity of residual variance. The results for performance, carcass traitsand meat quality traitsindicate that the regression coefficient of the intercept (b0) was higher than the random regression coefficient (b1). Heritability and additive genetic variance were influenced by the different tryptophan:lysine ratios of the diet. There was no genotype x environment interaction for the traitsof carcass yield, yield of breast and yield of thigh + overcoat. The quality traits of the meat CRA, b *, c * and H * (LF1) and CRA, PPC, L * and H * (LF2) presented genotype x environment interaction. It is possible to conclude that for yield traitsthe selection can be made in the lowest tryptophan: diet lysine ratios. For meat quality traitsthe sensitivity of the values indicates that the selection must be made in the tryptophan:lysine ratio in which the quails will be created.

Submitted by ANGEL DE JESUS LAZARO VELASCO null (angelstrauss26@hotmail.com) on 2017-10-25T17:49:03Z No. of bitstreams: 1 DissertacaoAngel.pdf: 1392488 bytes, checksum: 30d16b1c40935e0572a92a6d9c6dc400 (MD5) / Approved for entry into archive by Monique Sasaki (sayumi_sasaki@hotmail.com) on 2017-10-31T17:00:42Z (GMT) No. of bitstreams: 1 velasco_ajl_me_jabo.pdf: 1392488 bytes, checksum: 30d16b1c40935e0572a92a6d9c6dc400 (MD5) / Made available in DSpace on 2017-10-31T17:00:42Z (GMT). No. of bitstreams: 1 velasco_ajl_me_jabo.pdf: 1392488 bytes, checksum: 30d16b1c40935e0572a92a6d9c6dc400 (MD5) Previous issue date: 2017-09-26 / Consejo Nacional de Ciencia y Tecnología (CONACYT) / Há evidências na literatura que a uniformidade das características fenotípicas dos peixes, entre outros animais, pode ser afetada por componentes genéticos, além de fatores ambientais. Maior uniformidade na despesca é desejada, a fim de reduzir a competição entre os animais e, assim, ter uma produção mais homogênea, visando maior retorno financeiro da atividade. O objetivo deste estudo foi estimar se as variâncias residuais do peso e comprimento à despesca de tilápias do Nilo (Oreochromis niloticus) são afetadas por componentes genéticos, para avaliar a possibilidade de seleção para uniformidade de produção. Empregou-se o modelo hierárquico linear generalizado duplo (DHGLM) para calcular os componentes de variância, os parâmetros de herdabilidade, coeficientes de variação e correlações genéticas para peso (não transformado e com transformação Box-Cox) e comprimento à despesca. Foi utilizado um total de 8.725 informações fenotípicas de tilápias provenientes de 271 famílias da linhagem GIFT (Malásia), criados na estação experimental de piscicultura da Universidade Estadual de Maringá. Os resultados apoiaram a hipótese de heterogeneidade genética da variância residual para peso e comprimento à despesca, e a oportunidade de seleção medida através do coeficiente genético de variação da variância residual. Além disso, observou-se a necessidade de um grande número de filhos para a obtenção de estimativas precisas do mérito genético para variação residual, conforme indicado pelas estimativas de baixa herdabilidade. A transformação de Box-Cox foi capaz de diminuir a dependência entre a variância e a média do peso à despesca. A transformação reduziu, mas não eliminou toda a heterogeneidade genética da variância residual, destacando sua presença além do efeito da escala. / There is evidence in the literature that the uniformity of phenotypic traits of fish, among other animals, can be affected by genetic components, as well as environmental factors. Greater uniformity is desired in order to reduce competition among animals and thus have a more uniform production, aiming a greater financial return of the activity. The objective of this study was to assess if the residual variance of the weight and harvest length of the Nile tilapia (Oreochromis niloticus) is affected by a genetic component, to evaluate the possibility of selection for uniformity of production. The double hierarchical generalized linear model was used to estimate the components of variance, heritability, coefficients of variation and genetic correlation for weight (untransformed and with Box-Cox transformation) and harvest length. Phenotypic records of 8,725 individuals from 271 families were analyzed. The results supported the existence of genetic heterogeneity of residual variance on harvest weight and length, and the opportunity to select for increasing uniformity. Moreover, the low heritability estimates showed the necessity of high number of progeny for an accurate estimate of the genetic merit for the residual variance. The Box-Cox transformation of harvest weight reduced the dependency among its mean and variance. The transformation reduced but did not eliminate the genetic heterogeneity of residual variance, highlighting its presence beyond the scale effect. / CONACYT: 579742/410471

L’analyse de mesures longitudinales –appelées trajectoires– est de plus en plus fréquente en recherche médicale. L’un des intérêts de cette analyse est d’identifier des groupes d’individus ayant des trajectoires similaires. La classification obtenue peut être utilisée pour mieux comprendre l’hétérogénéité des évolutions entre individus. La classification peut être déterminée à partir d’un modèle pour lequel les trajectoires des individus correspondent à la trajectoire du groupe auquel ils sont affectés. L’objectif de la thèse est de développer une extension de ce modèle de classification standard permettant une meilleure prise en compte de la variabilité au sein des groupes, (i) variabilité des valeurs du marqueur (variance résiduelle) et (ii) variabilité des profils d’évolution (variance inter-individuelle). Deux modèles de classification sont développés : 1) un premier modèle qui prend en compte une variance résiduelle au sein de chaque groupe variable d’un groupe à l’autre, et 2) un deuxième modèle qui prend en compte une variabilité des trajectoires au sein des groupes au lieu de de prédire la même trajectoire pour tous les individus d’un même groupe, variabilité qui peut être identique ou variable d’un groupe à l’autre. L’intérêt de ces deux modèles a été montré par des travaux de simulations et par des applications cliniques. Globalement, lorsque le nombre de mesures et de trajectoires est suffisant, ces modèles donnent de meilleures classifications que celles du modèle de classification standard. Par ailleurs, en dehors de plans expérimentaux très contrôlés, les deux sources de variabilité sont inhérentes à la recherche en santé. Ces modèles sont donc très pertinents d’un point de vue clinique / The analysis of longitudinal measures –called trajectories– is more and more frequent in clinical research. One of the interests of this analysis is to identify groups of individuals with similar trajectories. The obtained classification is used to understand and explore the heterogeneity of trajectories among subjects. The classification can be performed by a model that predicts the same trajectory for all the subjects that are classified in the same group. The objective of this thesis is to develop an extension to the standard classification model that gives greater consideration to the variability within groups, (i) the variability of marker values (residual variance), and (ii) the variability of the individual trajectories inside a group (between-individual variance). Two classification models were developed: 1) a first model that allows unequal residual variance across groups, and 2) a second model that takes into account a between-individual variance within each group instead of predicting the same trajectory for all subjects in the same group, a variance that can be equal or unequal across groups. The interest of these two models has been studied by simulations and through clinical applications. Overall, when the number of trajectories and measurements per trajectory is sufficient, these models gives better classification compared to the standard classification model. Moreover, except for highly controlled experimental designs, the two sources of variability are inherent to research in health. Therefore, these models are very relevant from a clinical point of view.

Animal traits differ not only in mean, but also in variation around the mean. For instance, one sire’s daughter group may be very homogeneous, while another sire’s daughters are much more heterogeneous in performance. The difference in residual variance can partially be explained by genetic differences. Models for such genetic heterogeneity of environmental variance include genetic effects for the mean and residual variance, and a correlation between the genetic effects for the mean and residual variance to measure how the residual variance might vary with the mean. The aim of this thesis was to develop a method based on double hierarchical generalized linear models for estimating genetic heteroscedasticity, and to apply it on four traits in two domestic animal species; teat count and litter size in pigs, and milk production and somatic cell count in dairy cows. The method developed is fast and has been implemented in software that is widely used in animal breeding, which makes it convenient to use. It is based on an approximation of double hierarchical generalized linear models by normal distributions. When having repeated observations on individuals or genetic groups, the estimates were found to be unbiased. For the traits studied, the estimated heritability values for the mean and the residual variance, and the genetic coefficients of variation, were found in the usual ranges reported. The genetic correlation between mean and residual variance was estimated for the pig traits only, and was found to be favorable for litter size, but unfavorable for teat count.

abstract: Through a two study simulation design with different design conditions (sample size at level 1 (L1) was set to 3, level 2 (L2) sample size ranged from 10 to 75, level 3 (L3) sample size ranged from 30 to 150, intraclass correlation (ICC) ranging from 0.10 to 0.50, model complexity ranging from one predictor to three predictors), this study intends to provide general guidelines about adequate sample sizes at three levels under varying ICC conditions for a viable three level HLM analysis (e.g., reasonably unbiased and accurate parameter estimates). In this study, the data generating parameters for the were obtained using a large-scale longitudinal data set from North Carolina, provided by the National Center on Assessment and Accountability for Special Education (NCAASE). I discuss ranges of sample sizes that are inadequate or adequate for convergence, absolute bias, relative bias, root mean squared error (RMSE), and coverage of individual parameter estimates. The current study, with the help of a detailed two-part simulation design for various sample sizes, model complexity and ICCs, provides various options of adequate sample sizes under different conditions. This study emphasizes that adequate sample sizes at either L1, L2, and L3 can be adjusted according to different interests in parameter estimates, different ranges of acceptable absolute bias, relative bias, root mean squared error, and coverage. Under different model complexity and varying ICC conditions, this study aims to help researchers identify L1, L2, and L3 sample size or both as the source of variation in absolute bias, relative bias, RMSE, or coverage proportions for a certain parameter estimate. This assists researchers in making better decisions for selecting adequate sample sizes in a three-level HLM analysis. A limitation of the study was the use of only a single distribution for the dependent and explanatory variables, different types of distributions and their effects might result in different sample size recommendations. / Dissertation/Thesis / Doctoral Dissertation Educational Psychology 2016