Bivariate linear models in neurobiology: problems of concept and methodology

Hofman, Michel A.; Laan, Alfons C.; Uylings, H.B.M.

doi:10.1016/0165-0270(86)90114-7

Cited by 58 publications

(14 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Notice that the standard major axis is inappropriate for predictive purposes [Hofman et al, 1986). Variable x, in all equations, denotes brain volume (cm'), ranging from 0.1 to 4,200 cm' in surface equations, and from 0.1 to 1.500 env' in all other equations.…”

Section: Discussionmentioning

confidence: 99%

“…The variance of the estimated quantity can be computed from the additional statis tical information [see Hofman et al, 1986).…”

Section: Discussionmentioning

confidence: 99%

“…The stan dard major axis, in addition, is symmetrical and invariant with changes of scale. However, when one of the variables is fixed, and the other varies from natural causes, as in predictive models (see Appendix), the standard major axis has been shown to be an inap propriate method for describing bivariate distributions [Hofman et al, 1986], and ordinary linear regression was used instead.…”

Section: Statisticsmentioning

confidence: 99%

“…Since the variables were subject to both biological fluctua tions and errors of measurement, the standard (or reduced) major axis was preferred to the conventionally used method of linear least-squares regression analysis [Hofman et al, 1986). The stan dard major axis, in addition, is symmetrical and invariant with changes of scale.…”

Section: Statisticsmentioning

confidence: 99%

See 3 more Smart Citations

Size and Shape of the Cerebral Cortex in Mammals

1988

Self Cite

View full text Add to dashboard Cite

The geometry of the brain and cerebral cortex in mammals has been studied from an evolutionary perspective and is described in mathematical terms. The volume of the cerebral cortex, in contrast to the cortical surface area, scales to brain volume in a similar way, irrespective of the degree of cortical folding. Among mammals, Cetacea form a subgroup, in that their volumetric data fit an isometric model better than an allometric model. An index of corticalization is presented which contains information about both the mass of interconnective nerve fibers and the degree of intracortical processing. It is shown, furthermore, that a semilogarithmic equation appropriately describes the relationship between mean cortical thickness and brain volume. Finally, allometric equations between brain volume and cortical parameters, which can be used for predictive purposes, are presented.

show abstract

Section: Discussionmentioning

confidence: 99%

“…The variance of the estimated quantity can be computed from the additional statis tical information [see Hofman et al, 1986).…”

Section: Discussionmentioning

confidence: 99%

Section: Statisticsmentioning

confidence: 99%

Section: Statisticsmentioning

confidence: 99%

See 2 more Smart Citations

Size and Shape of the Cerebral Cortex in Mammals

1988

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since in most cases the variables are subject both to biological fluctuations and to errors o f measurement, the standard (or reduced) major axis (also called the geometric mean regression line) is preferred to the conventionally used method o f lin ear regression [Ricker, 1984]. An objection raised against the use of this method [Jolicceur and Heusner, 1971] in favor o f the ordinary major (= principal) axis, however, is that the slope of the standard major axis is almost insensitive to the strength o f the rela tionship, as reflected by the Spearman correlation coefficient r [Hofman et al, 1986]. However, as the correlation (r) approaches unity, as in the present study (r>0.99), the standard major axis and the principal axis will converge.…”

Section: Mathematical Proceduresmentioning

confidence: 99%

Size and Shape of the Cerebral Cortex in Mammals

Hofman¹

1985

Brain Behav Evol

Self Cite

221

110

View full text Add to dashboard Cite

The evolution of the brain in mammals has been accompanied by a progressive enlargement of the cerebral cortex. Allometric analysis of the volume, surface and convolutedness of this cortex shows that among mammals two major groups can be distinguished: (1) species with lissencephalic brains, where surface-volume relationships are determined by linear geometric laws, and (2) species with gyrencephalic brains, where strict geometric similarity no longer applies. Different mathematical models are required to describe the brain morphology in these groups. It has been shown, moreover, that among species with convoluted brains, marine mammals (Cetacea) form a subgroup in that the cerebrocortical surface in these animals is more folded than in terrestrial mammals of similar brain size. Thus it appears that the use of a single allometric relation in studying the effect of size increase on the geometry of the brain – irrespective of convolutedness or ecological strategy – as has been done in previous studies, is unjustified and obscures the differences in the structural organization of mammalian brains. Finally, a dimensionless index of cortical folding is proposed, which indicates that the degree of cortical folding depends not only on the volume of the brain or cortex but on cortical thickness as well.

show abstract

Use and misuse of the reduced major axis for line‐fitting

Smith

2009

American J Phys Anthropol

626

565

View full text Add to dashboard Cite

Many investigators use the reduced major axis (RMA) instead of ordinary least squares (OLS) to define a line of best fit for a bivariate relationship when the variable represented on the X-axis is measured with error. OLS frequently is described as requiring the assumption that X is measured without error while RMA incorporates an assumption that there is error in X. Although an RMA fit actually involves a very specific pattern of error variance, investigators have prioritized the presence versus the absence of error rather than the pattern of error in selecting between the two methods. Another difference between RMA and OLS is that RMA is symmetric, meaning that a single line defines the bivariate relationship, regardless of which variable is X and which is Y, while OLS is asymmetric, so that the slope and resulting interpretation of the data are changed when the variables assigned to X and Y are reversed. The concept of error is reviewed and expanded from previous discussions, and it is argued that the symmetry-asymmetry issue should be the criterion by which investigators choose between RMA and OLS. This is a biological question about the relationship between variables. It is determined by the investigator, not dictated by the pattern of error in the data. If X is measured with error but OLS should be used because the biological question is asymmetric, there are several methods available for adjusting the OLS slope to reflect the bias due to error. RMA is being used in many analyses for which OLS would be more appropriate.

show abstract

Bivariate linear models in neurobiology: problems of concept and methodology

Cited by 58 publications

References 29 publications

Size and Shape of the Cerebral Cortex in Mammals

Size and Shape of the Cerebral Cortex in Mammals

Size and Shape of the Cerebral Cortex in Mammals

Use and misuse of the reduced major axis for line‐fitting

Contact Info

Product

Resources

About