# LavPredict, Confidence Interval

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### Daniella

Jun 12, 2020, 5:10:05 AM6/12/20
to lavaan
Hi all,

I have a quick question: When I use lavPredict for the prediction of individual growth trajectories within an LGM, how can I get confidence intervals indicating whether the predicted individual growth trajectories are significantly different from zero?

I just can't seem to get my head around it

Thanks a lot for your help!

Best

### Terrence Jorgensen

Jun 12, 2020, 5:55:13 AM6/12/20
to lavaan
how can I get confidence intervals

You can set the argument se = "standard", then use those SEs (which are the same for each subject) to manually calculate your CIs.

Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam

### Daniella

Jun 12, 2020, 7:02:13 AM6/12/20
to lavaan
Dear Terrence,

thank you a lot for your very quick response. I actually first calculated the confidence intervals as you said (CI = Slope_individual +/- 1.96* SEM_individual)
but then found that out of 243 only 7 have a significantly different slope from zero. This confused me because the average slope over all individuals (in the LGM) is significantly different from zero. Since it seems to be the right way to do this, I guess these are correct results :)

So anyway, thanks a lot for you advice! That was very helpful.

### Yves Rosseel

Jun 13, 2020, 1:11:42 AM6/13/20
> thank you a lot for your very quick response. I actually first
> calculated the confidence intervals as you said (CI = Slope_individual
> +/- 1.96* SEM_individual)
> but then found that out of 243 only 7 have a significantly different
> slope from zero. This confused me because the average slope over all
> individuals (in the LGM) is significantly different from zero.

For the 'average' slope, we have 243 values, we can take a mean, and the
confidence interval for the average slope will be fairly narrow.
However, for the slope of an individual, we don't have a lot of
information, and the confidence intervals for the individual slopes will

Yves.

### Daniella

Jun 15, 2020, 7:10:43 AM6/15/20
to lavaan
Dear Yves, thank you very much for the clarification. Are there any other recommendations to evaluate whether such individual slopes are meaningful (non-zero)?

### Patrick (Malone Quantitative)

Jun 15, 2020, 9:09:30 AM6/15/20
Daniella,

If you have a lot of observations per person (you haven't said), you'll have more power for person-level slopes. Otherwise, it is what it is.

It's also not a question I've commonly seen addressed outside time-series research, for what it's worth.

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### Daniella

Jun 16, 2020, 6:03:32 AM6/16/20
to lavaan
Dear Patrick,

thanks a lot for your insights. I really appreciate the kind help in this forum. Unfortunately, I  only have 4 measurement points per person (over two years). In fact, I tried to reproduce the approach in a paper (Maia et al., 2016, JOB) with a similar setting (3 time points over three years) that says:

"To test hypotheses, we calculated the value of the latent variable of change for each individual using LGM. We then partitioned the sample into three groups: individuals with negative, positive, and zero time parameters. [...] Zero time parameters were established while assuming a 98 per cent confidence interval around zero. Note that this is a rather strict assumption and implies a conservative testing of our hypotheses."

That is why I have tried to establish the confidence intervals around the individual slopes. But it seems to me that I don't have enough variance in the slopes between subjects, or the author meant something different with "98 per cent confidence interval around zero".

Either way, I agree with you that this is probably not the most common procedure. Nevertheless I liked it, so I tried to replicate it with my data, but so far I haven't been very successful :)

Am Montag, 15. Juni 2020 15:09:30 UTC+2 schrieb Patrick (Malone Quantitative):
Daniella,

If you have a lot of observations per person (you haven't said), you'll have more power for person-level slopes. Otherwise, it is what it is.

It's also not a question I've commonly seen addressed outside time-series research, for what it's worth.

On Mon, Jun 15, 2020 at 7:10 AM Daniella <daniela....@gmail.com> wrote:
Dear Yves, thank you very much for the clarification. Are there any other recommendations to evaluate whether such individual slopes are meaningful (non-zero)?

Am Samstag, 13. Juni 2020 07:11:42 UTC+2 schrieb Yves Rosseel:
> thank you a lot for your very quick response. I actually first
> calculated the confidence intervals as you said (CI = Slope_individual
> +/- 1.96* SEM_individual)
> but then found that out of 243 only 7 have a significantly different
> slope from zero. This confused me because the average slope over all
> individuals (in the LGM) is significantly different from zero.

For the 'average' slope, we have 243 values, we can take a mean, and the
confidence interval for the average slope will be fairly narrow.
However, for the slope of an individual, we don't have a lot of
information, and the confidence intervals for the individual slopes will

Yves.

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