Standardized path coefficient greater than 1

joanna paczkowska

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Feb 5, 2020, 9:16:22 AM2/5/20

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Dear All

I would like kindly to ask for a help with my model. I run a model including data from my experiment where I look on impact of phosphate and DOC on microbial community:

Model: I have primary production, bacterial production, zooplankton and ciliates

Model1<-' PP ~ DOC+PO4+BB

Zoo ~ PP+Ci+BB+DOC

Ci~ BB+PO4+DOC

BB~ DOC+PO4

'

Model1<-sem(Model1, data=GLM_Model_River_Project, meanstructure=TRUE)

summary(Model1, rsquare=T, standardized=T)

Results looks nice however I received standarized path coefficient greater than 1. (1.03). I found that it can be possible because of multicolliniary or small size of samples. I checked VIP results and all are below 10. My question is - is it even possible to publish data with standarized path coefficient greater than 1. Or i received some artificial effect. I know that a lot of people only looking on my results which immediately suggest that it is wrong.

I will be extremely grateful for your help.

Joanna

Model Test User Model:

Test statistic 0.395

Degrees of freedom 2

P-value (Chi-square) 0.821

Parameter Estimates:

Information Expected

Information saturated (h1) model Structured

Standard errors Standard

Regressions:

Estimate Std.Err z-value P(>|z|) Std.lv Std.all

PP ~

DOC -0.090 0.043 -2.097 0.036 -0.090 -0.410

PO4 -1.538 1.086 -1.416 0.157 -1.538 -0.291

BB 0.071 0.093 0.762 0.446 0.071 0.132

Zoo ~

PP 12.468 7.927 1.573 0.116 12.468 0.255

Ci 21.860 24.327 0.899 0.369 21.860 0.218

BB 3.063 3.533 0.867 0.386 3.063 0.117

DOC -8.008 2.865 -2.795 0.005 -8.008 -0.749

Ci ~

BB 0.000 0.027 0.012 0.991 0.000 0.001

PO4 -0.951 0.313 -3.038 0.002 -0.951 -0.368

DOC 0.110 0.012 8.904 0.000 0.110 1.028

BB ~

DOC -0.095 0.092 -1.028 0.304 -0.095 -0.232

PO4 4.269 2.228 1.916 0.055 4.269 0.433

Intercepts:

Estimate Std.Err z-value P(>|z|) Std.lv Std.all

.PP 1.262 0.295 4.281 0.000 1.262 4.104

.Zoo 52.026 19.201 2.710 0.007 52.026 3.455

.Ci -0.522 0.085 -6.137 0.000 -0.522 -3.470

.BB 1.837 0.530 3.463 0.001 1.837 3.196

Variances:

Estimate Std.Err z-value P(>|z|) Std.lv Std.all

.PP 0.059 0.017 3.464 0.001 0.059 0.624

.Zoo 94.408 27.253 3.464 0.001 94.408 0.416

.Ci 0.005 0.001 3.464 0.001 0.005 0.217

.BB 0.287 0.083 3.464 0.001 0.287 0.867

R-Square:

Estimate

PP 0.376

Zoo 0.584

Ci 0.783

BB 0.133

Graph8_Manuscript.jpg

Terrence Jorgensen

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Feb 5, 2020, 3:38:48 PM2/5/20

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is it even possible to publish data with standardized path coefficient greater than 1.

Yes. It is not a contradictory result.

Or i received some artificial effect.

Did you receive a warning message about your variables having very different scales? Looking at your residual variances, I would expect Zoo to have a much larger influence on the optimizer because its variance is so much larger. The standardized slope > 1 has an exogenous predictor, so I cannot see anything about its scale. Maybe try multiplying small-variance variables by 10 or dividing Zoo by 10 to get rid of the error, and see if it converges on a different solution. Even if it does not, there is nothing necessarily wrong with these results.

I know that a lot of people only looking on my results which immediately suggest that it is wrong.

You can refer reviewers to this post about how it is possible: https://stats.stackexchange.com/questions/120201/magnitude-of-standardized-coefficients-beta-in-multiple-linear-regression

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

joanna paczkowska

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Feb 6, 2020, 9:35:26 AM2/6/20

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Dear Terrence

Thank you very much for you answer. I really appreciate it:) I will divide my zooplankton data as you suggested :) And if it doesn't change anything I will accept my results.