I want to know how to interpret this scatter plot.
Thanks in advance.
Reference:
(Nutrients. 2014 Dec 22;6(12):6005-19. doi: 10.3390/nu6126005.)
It's hard to know without seeing the caption, but assuming the curved lines are showing a 95% confidence interval around the regression line, then this looks like a typical scatterplot, showing that RRs gets lower as magnesium intake gets higher. I don't know if bigger circles mean more data in that sample, or what; the caption for the figure probably explains this.
The paper is available online. Caption is:
"Association between the risk of metabolic syndrome and dietary magnesium intake: dose-response meta-regression. The levels of magnesium intake (mg/day) were modeled using a linear trend with random-effects meta-regression models. The solid black line represents the weighted regression line based on variance-weighted least squares. The gray line shows the 95% CI around the regression line. The circles indicate RRs in each study. The circle size is proportional to the precision of the RR. The vertical axis is on a log scale."
"As shown in Figure 2a, for the ten epidemiological studies that assessed dietary magnesium intake, the pooled estimate indicated that magnesium intake (mg/day) was significantly and inversely associated with metabolic syndrome based on the meta-regression model, as follows:"
Mohamed -
Further comments:
1) Congratulations with your attention to scatterplots. They can be very useful, providing insight.
2) What appear to be 'outliers,' high on the left, and low on the right, make me wonder if there might be a very important missing independent variable, giving you substantial omitted variable bias here.
3) If you had weighted least squares regression prediction intervals on the dependent variable 'errors,' then perhaps it would show, more clearly, how noisy the data are. ??? I don't know if this is applicable to this kind of graph.
4) How would you interpret your intercept? When magnesium intake is zero, does it make sense to say that ln(RR) = 0.164 (whatever "RR" is)? What does it mean to have negative magnesium intake? I mean, perhaps your scatterplot is only approximately linear, and only in a limited range, such as when analytical chemists talk about equipment calibration. Might you be better off with a loess model? Or splines?
[Salvatore, I am not familiar with this particular kind of scatterplot and this application. You mention the circles indicate precision of the "RRs" (whatever they are), so I assume you mean variance alone (not bias). You mention weighted regression, but the line looks like an OLS regression with emphasis on mean. I'd appreciate it if you could clarify this for me a little. - Also, I see "RR" on the y-axis, but ln(RR) in Mohamed's equation. Did you interpret that as a mistake?]
Was the log used to reduce heteroscedasticity? I prefer to keep that in the error structure where it naturally occurs - and estimate a useful coefficient of heteroscedasticity - rather than transform, as transformed data are less clearly interpretable. As transformations go, however, depending upon your application, "ln" is often a useful one.
Thanks for an interesting graph. Perhaps you can tell us all later how this all turns out.
Cheers - Jim
PS - Ah. Looking up the doi for that paper, it seems "RR" is "hazard rate ratio." Ratios of variables can be tricky. I like to look at the numerator and denominator separately, but am not expert in survival data, if that is what this is about, so I assume there must be good reasons for looking at the ratio as one variable ... but I wonder.
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