The output depends on the particular software used, so check that, but negative path loadings are often associated with inverse relationships, so as X increases, Y tends to decrease (conditional on what else is in the model).

Melissa, we need more information. Are the first-order factors all positively related or not? Are the correlations all large or are some small?

Regards, Karin 

I guess you employed Amos Graphic for your analysis. 

The negative factor loading from the second order construct to the corresponding first order indicate the second order construct reflected negatively on its first order construct. We should call second order construct is a construct while the first order constructs as components. Since the construct is latent reflective, we can say that the construct reflected negatively on one of its component. This is trus provided that all items have positive factor loading.

Thanks @Daniel, I'm just worried that this inverse relationship signifies a problem since my other lower-order factors have got positive path loadings. 

Thanks @Karin, the first-order factors are all positively correlated to each other, except with this factor (let's call it factor B). It's only positively correlated to one other factor (weakly). Most other correlations are moderate to large, as shown below (A-H are my lower order factors, there's no factor D).

Correlations: 

A B -.242

A C .401

A F .624

A G .755

A H .554

E A .479

B C -.167

B F -.353

B G -.219

B H .100

E B -.476

C F .295

C G .492

C H .630

E C .314

F G .665

F H .324

E F .422

G H .581

E G .358

E H .199 

Thanks in advance for your advice!

Its no harm for getting negative correlation between constructs. I though you were talking about negative factor loading. Your question is ambiguous. Please clarify properly. You cannot assume everybody knows as much as you do since this is your work.

Thanks for your input @Zainudin. I was answering @Karin's question about the correlation between factors / constructs. My question is about a negative factor loading as stated. 

Melissa, the correlations clearly indicate that factor B is negatively correlated with almost all factors (with the exception of factor H, but this is a small correlation). The remaining factors A to H are all positively correlated. Therefore your result is what one would expect: All positively correlated factors have positive factor loadings on the second-order factor, and factor B has a negative factor loading. Is it possible that the items of factor B are reverse coded?

Just think about a factor model with emotion factors anxiety, depression, worry, and also happyness. The higher-order factor would be a negative emotion factor, and happyness would have a negative factor loading.

Therefore I would suggest that you check the content of your items / scales. Does a reverse coded factor make sense?

Kind regards, Karin

Since this is a CFA, you must have assigned the items to Factor B, so you know something about their content (such as whether they were all reversed). 

Possibly, if you developed your constructs from an Exploratory Factor Analysis, you Factor B could represent some kind of "method factor" where those items all have something similar about the way that they were asked.

Dear Melissa,

I agree with Karin with regards to reverse coding.  If you are using primary data collected from a survey for your analysis, ensure that the coding is consistent such that any negative statements are reverse coded.  This might solve your problem if this was the reason why you got the negative values.

Everybody need to understand here that all items have positive factor loading. So the negatively worded statement and reverse coding do not arise.

The factor loading for all items are positive but the factor loading for one of the components is negative. That is the question asked.

In this case what I said yesterday was correct. The construct reflect negatively on that particular component. And nothing is wrong.

Reversing the coding will get the factor loading for component to be positive but will result in all items to have negative factor loading.

Thanks Karin, David, Kamarul, and Zainudin for your valuable input. Sorry for the delayed response, am still trying to figure this out. 

I didn't realize that my question could have been unclear. I didn't mention that my item loadings were all positive. I hope the below helps illustrate my model better:

• Items (+) -> factor B (-) -> construct                                                              
• Items (+) -> all other factors (+) -> construct

I have thought about reverse coding, but the items for factor B are not to be reverse coded. Which was why the negative loading puzzled me. If I had forgotten to reverse code, though, that would make all factor B's item loadings negative too (not only factor B's loading), is that right?

In terms of content, my higher-order construct is adolescent maladjustment, with lower-order factors like negative self-esteem, aggression, and so on. Factor B is dependence. According to the IPARTheory that I'm basing my hypothesis on, adolescents who are maladjusted are dependent. But if the loading for this factor is negative, that means that maladjusted adolescents are independent instead, which made me worried that there's something wrong somewhere that I cannot figure out. Or have I misunderstood what this negative loading meant?

This is an established scale that I did not develop. I have not found any journals that found such negative loading. Perhaps I should look further.. 

Melissa, from a statistical point of view the higher-order loading must be negative because this factor is negatively correlated with all other factors. If your items are coded in the direction of dependence (and not independence?), then enhancing dependence by one unit reduces adolescent adjustment by the negative path coefficients.

If this result is not according to theory, you should have a look at the items, their content and their coding.

Using an established scale does not mean that this scale is also suitable for your sample.

Hope this helps.

Regards, Karin

Oh, I did a mistake: Increasing adolescent adjustment by one unit reduces dependence by the amount of the path coefficient. The arrow goes from the second-order construct to the lower order construct.

Regards, Karin

Thanks Karin! I apologize, I made a mistake in my answer (which I've just edited), the higher order construct is adolescent maladjustment rather than adjustment, sorry for the confusion. 

My items are coded in the direction of dependence. And dependence is supposed to be positively correlated to maladjustment, but the loading is negative, which means increasing maladjustment by one unit reduces dependence by the amount of the path coefficient, is that right? 

And since this is the result that I got, can I attribute the 'abnormal' sign to my sample? (After I've checked items' content and coding)?

Have you reverse the coding?

You need to get the factor loading for all items to be positive first.

Melissa, your higher-order factor model does not fit well. I just checked a small model with A - H as indicators of a single factor, and the model fit was bad. Furthermore, the residual variances are quite high for B, C, E, and H, indicating that there are other factors influencing these variables besides the common factor.

Modification indices point to omitted covariances between the first-order factors: B with E and H, C with H. The covariances between the residuals of these factors have to be added in order to enhance model fit.

Therefore, I guess that the complete model does not fit the data? Then, you cannot interpret any coefficients as they may not be valid in the population.

It is obvious that a one-factor-model does not fit the data.

Hope this helps, Karin

Thanks a lot for the heads up, Karin! I'll PM you for further discussion..

Hi Mellissa,

Were you talking about negative correlations (covariances) between two latent variables after running CFA?

*Melissa