Separating the continuous predictor 'time' into 3 categories is not actually more finely assessing the association. On the contrary, it becomes a more coarse analysis because you're losing a great deal of information (variability) by converting a continuous variable into a discrete variable.

When you convert 'time' into a categorical variable with 3 levels, the coefficient no longer reflects the rate of change in depression - since the predictor (time) is no longer continuous. The coefficients now reflect the mean differences among the groups. If the 0-18 year group shows a significant p-value, this means this group's average depression score is significantly different from one (or both) of the other 2 groups. If the coefficient is negative, this means the 0-18 year group's average depression score is significantly lower than one (or both) of the other 2 group's average depression score.

Ningbo Kou -

Forget about the p-values. With different sample sizes, they are not comparable.

You didn't say if the signs were still negative in each group. A small sample size may give you a fluke result, and there could be collinearity. People living in rural areas for one of those time periods may or may not be in part of one or more other time period groups. Results could be hard to interpret. Still, I'd be interested in how many groups had negative coefficients, but with small samples you could have a large standard error, so I'd look at the standard errors, even though those could be somewhat questionable with the cross-overs in categories.

Perhaps your most useful result is the one with no age breakdown. But I wonder also, are there no other relevant variables? In general, if you leave out relevant predictors, you bias results. If you put in extraneous predictors, you increase variance. You don't want too many, or too few variables, but just the right ones, and I'm referring to the time in a rural setting as one variable. Is there anything else, from your subject matter experience, which could be relevant?

Best wishes - Jim

PS -

My guess is that there are more people in the 0-18 age group, because this includes those who live in a rural setting all their lives, and those who are born there, but leave. I suspect that more people are born in a rural setting and leave than are born in an urban setting and move to a rural one. With a larger sample size in the 0-18 age group, you are more easily able to find "significance," but that is an illusion. It is why I have a letter published in The American Statistician from the late 1980s on this topic, because a p-value is commonly misinterpreted. Standard errors also are impacted by sample size, but are easier to interpret well enough. Forget about p-values. They are not a good stand alone statistic.

Cheers.

Dear James R Knaub

I may have caused some misunderstanding due to my poor expression. In this study, my research subjects are residents aged 65, so the various age segments of residential duration are actually a retrospective of their residential history (for example, "residency duration from 0 to 18 years of age" means how long these 65-year-old individuals lived in rural areas during the ages of 0-18). Therefore, dividing the age segments only converts one variable into multiple variables without changing the sample size.

Indeed, I included additional variables in my model. Apart from variables reflecting personal characteristics, I also included "currently residing in a rural area," "duration of local residence," and "interaction term between duration of rural residence and poor rural area" as variables. Furthermore, the model I used was based on a database, so the sample size was around 6000 cases. However, most residents in my sample rarely move, so the residential duration of most people may be relatively extreme. Regarding the issue of collinearity, I encountered this problem during the model construction, and I addressed it using ridge regression.

I noticed that the "rural residence time" for all age segments is negative, although only the 0-18 age segment reached significance (the standard errors of segmented variables are around 0.5, compared to 0.77 without segmentation; forgive me for not being very clear on the meaning of standard errors). Therefore, I agree with your statement that residential duration has an impact on depression from the perspective of the entire time period, but after segmentation, only the 0-18 age group has a sufficient sample size to capture significance.

So, can I conclude that the length of rural residence has an impact on depression, with a particularly strong effect during the 0-18 age range?

Thank you for your response to my question!

Dear Blaine Tomkins

Forgive my clumsy expression, but what I actually did was to convert one variable into multiple variables, rather than turning it into a categorical variable. Specifically, the age ranges of 0-18, 18-29, and 29-45 years are three separate continuous variables. The research subjects, on the other hand, are elderly individuals aged 65, and the aforementioned variables can be understood as their recollections of their residential experiences during different time periods.

Best wishes - Kou

You say "...(for example, "residency duration from 0 to 18 years of age" means how long these 65-year-old individuals lived in rural areas during the ages of 0-18)." Sorry. You are correct that for multiple regression they would all be included. So if it was zero years, you count them in that sample. But there are probably fewer zeroes for the number of years lived by a 65-year-old in the 0-18 category, as I explained above, perhaps providing more useful data for that category. Zeroes may be problematic here. Regression involving counts may be done differently, and not in my expertise, but might be useful here.

By the way, are your 65-year-olds currently residents anywhere, or are you only looking at 65-year-old current rural residents (because that would make a difference)?

The only other comment that occurs to me is that I think you want to be careful not to make too much of your results. You might even want to separate your study into different parts with different models, perhaps.

Dear James R Knaub

I included all samples (rural and non-rural) in the model, and I actually agree with you that there are more extreme data in the 0-18 age group variable which makes it seem easy to become significant , after all I think residents of other age groups move less often. I now decided to find some medical papers, their research may cover similar content, such as long-term and age-specific drinking effects on health and so on. Otherwise, I think it may be necessary to split my research into two different parts. Anyway, thank you very much for your answer

Best wishes

Best wishes.

Based on your description, you did not split one variable into multiple variables. Rather, you split your sample and ran 3 separate models each with a different subset of participants. Correct me if I'm wrong.

Dear Blaine Tomkins

Sorry, what I actually meant is to divide the variable of a person's "past residential experiences" into four segments, which means examining the impact of the residential experiences during the ages of 0-18 and 18-29 etc on their current depression. These four variables are explained within the same model.

Ningbo Kou It would be much easier if you provide the full output of your regression