It is usually said (at least in epidemiological terms) that in a linear regression the intercept (bo) has no real biological significance when revealing a linear relationship between continuous outcome and independent variable/s. Now assume you have a situation wherein you want to know/compare the rate at which an outcome is recorded following the quantity of a product consumed, ain't (bo) not worth considering there?
If the intercept is of no importance in your research, you could standardize the variables (transform to z) and eliminate the intercept. This would provide more direct information regarding the relationships between the dependent variable and the independent variable(s).
I think, what Jia means is the interpretation of the intercept and not whether to use an intercept or a no intercept model.
The intercept has a meaningful interpretation if X=0 falls within the range of the X values in the experiment. Say, X=dose of medicine, where in the experiment x=0,5,10,15,20.25, and the response variable is body temperature. Here, the intercept means: "the expected body temperature when no medicine is given".
If the X values in the experiment do not cover zero, then the interpretation of the intercept is simply "the point at the Y axis through which the regression line passes".
I hope that this is helpful.
Quiet correct Raid...i doesn't add to common sense when some people keep saying that the intercept has no biological meaning in a correlation association. you answer speaks volume of the relevance of an intercept only model
I think it depends on your case. Sometimes, b0 has special meaning, and sometimes, it is better to set b0=0. These two situations can be defined as regression estimation and ratio estimation respectively. For example:
(1) biomass = b0 + b1*volume for single tree, b0 means the biomass of a tree with 1.3m height.
(2) biomass = b1*wet weight for single tree, b0=0 and b1 means the moisture content.
Therefore, it is necessary to analyze whether or not b0 has real biological significance.
I hope this is helpful to you. Good luck!
It is true that in using standardized scores , the intercept is zero because variables measured in standardized scores have zero average. But if variables are measured in unstandardized scores then the interpretation of b0 becomes very important.
First of all , the constant b0 is the intercept, i.e. the value of Y when X is zero. It is important to mention here that if bo is negative then, we have to interpret elasticity.
Elasticity = Percentage change in Y / Percentage change in X
η = (ΔY/Y) / (ΔX /X)
Since elasticity changes at each point of the function then, it is recommended to replace X and Y by their averages.
This means, that if bo = 0 then, elasticity is unitary. If bo < 0 then , it is
elastic , But if bo >0 then , it is inelastic. You can check pages 37-38 of my book:
Moreover, if we use dummy variable (D) -and we may use the interaction D*Xi using 1's and 0's for group membership in one regression run then, the advantage of using dummy variable model is the fact that this model enables us to test the significance of the shift in intercept ( significant D) and/or the significance of the change in slope ( significant X*D) as shown on page 90 of my book.
Furthermore, if you run ANOVA using regression then, bo is the average of the control group.
In sum, the interpretation of bo depends on your research problem and may give you very valuable information
It is true that in using standardized scores , the intercept is zero because variables measured in standardized scores have zero average. But if variables are measured in unstandardized scores then the interpretation of b0 becomes very important.
First of all , the constant b0 is the intercept, i.e. the value of Y when X is zero. It is important to mention here that if bo is negative then, we have to interpret elasticity.
Elasticity = Percentage change in Y / Percentage change in X
η = (ΔY/Y) / (ΔX /X)
Since elasticity changes at each point of the function then, it is recommended to replace X and Y by their averages.
This means, that if bo = 0 then, elasticity is unitary. If bo < 0 then , it is
elastic , But if bo >0 then , it is inelastic. You can check pages 37-38 of my book:
Moreover, if we use dummy variable (D) -and we may use the interaction D*Xi using 1's and 0's for group membership in one regression run then, the advantage of using dummy variable model is the fact that this model enables us to test the significance of the shift in intercept ( significant D) and/or the significance of the change in slope ( significant X*D) as shown on page 90 of my book.
Applied Econometrics using Eviews, SPSS & Excel with Applications in Arab Countries (2012). Available at AMAZON. First edition 10/2011; AuthorHouse Publishing (October 19, 2011)., ISBN: ISBN-10: 1456775790 ISBN-13: 978-1456775797
http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Dstripbooks&field-keywords=Charbaji
Furthermore, if you run ANOVA using regression then, bo is the average of the control group.
In sum, the interpretation of bo depends on your research problem and may give you very valuable information
How important is the intercept (bo) in linear regression interpretation? - ResearchGate. Available from: https://www.researchgate.net/post/How_important_is_the_intercept_bo_in_linear_regression_interpretation [accessed Dec 14, 2015].
For me the intercept term is a very important term - I am a multilevel modeler and I may literally have hundreds or indeed thousands of intercepts in a random intercepts model.
It is therefore important for interpretation (and sometimes for estimation) to parameterize the model so as to make for an informative intercept term . I teach these two rules
1 for continuous predictors, centre them on a typical average value eg on the median. So if the typical adult in the study is 46 ; a 30 year old is then given the value 30-46 that is minus 16, similarly a 56 year old has the deviated value of +10.
2 if you have categorical predictors and are using dummy reference coding choose the most common category ( the modal category) as the omitted base category. So if 60% of my sample are males and 40% are females - I include a female dummy in the the regression model and the zero value on the dummy refers to a male.
In fitting a basic (non multilevel) model I would have
Blood pressure = Intercept + Slope*(Age-46) + Differential For Females
The estimated intercept is then the average blood pressure for a 46 year old man - and I can then compare the other effects with this base.
It is an often-taught rule that you should not predict outside of the range of your explanatory variables - and if you do not centre ( as in Age-46) you would be extrapolating to a baby aged zero - and this would be inappropriate in a study of adult hypertension!
The case of not using a zero - regression through the origin- forces the predicted response (Y-Hat) to be zero when X is zero - this might be useful when the response is say an expensive way of measuring something and X is a cheaper alternative of measuring the same thing.
Kelvin, you recommend to use the most common category of a categorical predictor as reference. But what about effect coding? You would so get intercepts for the "means" of the categories, and (at least for balanced designs) interaction terms with this variable would be orthogonal.
Jochen - I agree and understand - I was careful to refer to reference coding and not balanced data (which is the usual in observational research) - I also point my students to these resources -
http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter5/statareg5.htm
as they can then see the many of the options open to them - my point was to emphasize the need for an interpretable intercept.
- Badges
- Science topic
- Similar topics
- Analytical Chemistry
- Column