Analyzing FS Scatters: Grip-Pulmonary

[andkov]

Our goal here is to see how intercepts and slopes are related. There are several indicators of that relationship.

• R - estimated correlation. We used this hack to request standardized covariances (correlations) of the focal parameters: TAU_00 and TAU_11. This is that parameters (for phys.cog continuity: R_IPIC and R_SPSC)
• R_pval - p-value associated with the R parameters. If it is small enough, we say that the parameter is significantly different from zero( there is a linear relationship).
• TAU_pval - the p-value of the TAU coefficient that R parameter is supposed to standardize. TAU is on the raw scale, so we can't really meaningfully compare coefficients across studies. But the significance tells us whether its (covariance between random terms) was a significant contribution to the model. If TAU_pval is small enough we can say that there is a linear relationship.
• r - is a correlation of the regression line, fitted through the scatter space of factor scores . Think of its square as the amount of variability explained in intercept/slope of the first process by the variability of the intercept/slope of the second process. The larger it is the stronger the linear relationship is.

I will use these four indices along with the fullness of the data in the graphs after the links to offer my judgement of how this relationship should be characterized.

Female

STUDY	intercept	rating	slope	rating
EAS	.29 (.05; .00) .33	mod +	.03 (.97; .19) .11	ns
ELSA	.25 (.00 ; .00) .61	strong +	.63 (.50; .10) .46	ns / weak +
HRS	.29 (.00; .00) .65	strong +	-.52 (.64, .50) .64	ns / weak +
ILSE
LASA	.28 (.01; .00) .54	strong +	.03 (.98; .95) .42	ns / weak +
NUAGE
OCTO	.39 (.00, .00) .49	strong +	.34 (.36; .05) .21	weak +
RADC	.19 (.00, .00) .42	mod +	.16 (.66; .53) .10	ns
SATSA	.06 (.59; .00) .49	mod +	.03 (.94; .10) .13	ns

Numerical summary used in the table:

• R : correlation coefficient estimated by Mplus (R_IPIC, R_SPSC)
• R_pval : p-value associated with the R parameters
• TAU_pval : p-value associate with the variance estimate of the random term (TAU_00, TAU_11)
• r : correlation of the regression line (red) through the scatter of the factor scores
• structure : R (R_pval, TAU_pval) r
• mod = moderate
• ns = non-significant
• "+" = positive relationship
• "-" = negative relationship

  Male

STUDY	intercept	intercept	slope	slope
EAS	.04 (.92; .05) .23	weak +	.08 (.97; .51) .21	ns
ELSA	.19 (.00 ; .00) .54	strong +	.42 (.22; .23) .42	ns / weak +
HRS	.11 (.16; .00) .61	strong +	-.16 (.89, .81) .54	ns / weak +
ILSE
LASA	.22 (.00; .00) .38	strong +	.57 (.00; .00) .32	strong +
NUAGE
OCTO	.15 (.29, .00) .18	mod +	.10 (.87; .08) .09	ns / weak +
RADC	.25 (.00, .00) .42	mod +	-.04 (.91; .29) .00	ns
SATSA	.21 (.04; .00) .55	mod +	.75 (.94; .10) .25	ns

[andkov]

With respect to the process pair "Grip-Pulmonary" it appears that
1) intercepts have a positive linear relationship, moderate to strong across studies. 2) there is little evidence to suggest that slopes of these two process are related. However, visual inspection suggested that a week positive relationship may be present. The statistical support for this view was provided only by a few instances (LASA-male; OCTO-female) and was weakened by a few suspicions in data/model misbehavior. One of the possible reasons for this misbehavior is considered to be a small variability of the slope in measures of these studies.

@ampiccinin , @annierobi , @GracielaMuniz , do these conclusions read well and reasonable to you?

[ampiccinin]

yes