PMC:4620161 / 23163-24697 JSONTXT

{"project":"0_colil","denotations":[{"id":"26578853-24954281-358040","span":{"begin":1297,"end":1301},"obj":"24954281"}],"text":"In other words, the m regression coefficients associated with the m basis functions from each subject are brought to the group level and treated as the instantiated values of m simultaneous variables. When the effect estimates associated with the basis functions of ESM or ASM are treated as the values of m simultaneous response variables, the hypothesis (2a) or (2b) can be analyzed through MVT under the model (1). Geometrically, the data for H01MVT represent the group centroid (α1, α2, …, αm) in the m-dimensional real coordinate space ℝm (Table 1), and the associated one-sample Hotelling T2-test is performed to reveal whether the group centroid lies in the rejection region (outside of an m-dimensional ellipse centering around the origin in the case of H01MVT). Similarly, the data for H02MVT are expressed as two group centroids, (α11, α12, …, α1m) and (α21, α22, …, α2m), and the corresponding two-sample Hotelling T2-test is conducted to see if the hypothesis (2b) about the two centroids can be rejected. The hypothesis (2b) can be easily generalized to the situation with more than two groups of subjects (e.g., three genotypes) as well as more than one subject-grouping variable (e.g., sex, genotypes, and handedness) through the formulation of general linear testing (Chen et al., 2014). One noteworthy feature of MVT is that it allows those simultaneous effects to have different scales or units, unlike the traditional AN(C)OVA or univariate GLM in which all the levels of a factor are usually of the same dimension."}

{"project":"TEST0","denotations":[{"id":"26578853-233-241-358040","span":{"begin":1297,"end":1301},"obj":"[\"24954281\"]"}],"text":"In other words, the m regression coefficients associated with the m basis functions from each subject are brought to the group level and treated as the instantiated values of m simultaneous variables. When the effect estimates associated with the basis functions of ESM or ASM are treated as the values of m simultaneous response variables, the hypothesis (2a) or (2b) can be analyzed through MVT under the model (1). Geometrically, the data for H01MVT represent the group centroid (α1, α2, …, αm) in the m-dimensional real coordinate space ℝm (Table 1), and the associated one-sample Hotelling T2-test is performed to reveal whether the group centroid lies in the rejection region (outside of an m-dimensional ellipse centering around the origin in the case of H01MVT). Similarly, the data for H02MVT are expressed as two group centroids, (α11, α12, …, α1m) and (α21, α22, …, α2m), and the corresponding two-sample Hotelling T2-test is conducted to see if the hypothesis (2b) about the two centroids can be rejected. The hypothesis (2b) can be easily generalized to the situation with more than two groups of subjects (e.g., three genotypes) as well as more than one subject-grouping variable (e.g., sex, genotypes, and handedness) through the formulation of general linear testing (Chen et al., 2014). One noteworthy feature of MVT is that it allows those simultaneous effects to have different scales or units, unlike the traditional AN(C)OVA or univariate GLM in which all the levels of a factor are usually of the same dimension."}

{"project":"2_test","denotations":[{"id":"26578853-24954281-38285029","span":{"begin":1297,"end":1301},"obj":"24954281"}],"text":"In other words, the m regression coefficients associated with the m basis functions from each subject are brought to the group level and treated as the instantiated values of m simultaneous variables. When the effect estimates associated with the basis functions of ESM or ASM are treated as the values of m simultaneous response variables, the hypothesis (2a) or (2b) can be analyzed through MVT under the model (1). Geometrically, the data for H01MVT represent the group centroid (α1, α2, …, αm) in the m-dimensional real coordinate space ℝm (Table 1), and the associated one-sample Hotelling T2-test is performed to reveal whether the group centroid lies in the rejection region (outside of an m-dimensional ellipse centering around the origin in the case of H01MVT). Similarly, the data for H02MVT are expressed as two group centroids, (α11, α12, …, α1m) and (α21, α22, …, α2m), and the corresponding two-sample Hotelling T2-test is conducted to see if the hypothesis (2b) about the two centroids can be rejected. The hypothesis (2b) can be easily generalized to the situation with more than two groups of subjects (e.g., three genotypes) as well as more than one subject-grouping variable (e.g., sex, genotypes, and handedness) through the formulation of general linear testing (Chen et al., 2014). One noteworthy feature of MVT is that it allows those simultaneous effects to have different scales or units, unlike the traditional AN(C)OVA or univariate GLM in which all the levels of a factor are usually of the same dimension."}