I am quite new to R and coding so please forgive the lack of in depth information I may provide. I am also new at using linear models, particularly with large data sets. I have used the gls function in the nlme package to assess water quality data and I just need to understand the output and what I need to report for an article.
I want to look at the relationship between water flow and various parameters (electrical conductivity, pH etc etc) over a long time period (50 years). The data is stationary and there are many data points so autocorrelation is present (I tested for this elsewhere) and this is why I am using gls instead of linear methods (was also suggested to me by a reviewer for a paper). I ran the code to look at flow and electrical conductivity (ec) and the dataset name is rivin.
I ran a first model
(m1) using the following script
and then a second one as follows using the AR(1) function
I then used
anova() to check significance between the two models and this is the output:
Model df AIC BIC logLik Test L.Ratio p-value m1 1 3 183.2906 193.5522 -88.64531 m2 2 4 164.8020 178.4841 -78.40098 1 vs 2 20.48866 <.0001
Does this mean that
m2 is significantly different from
I then look at the summary from
summary(m2) Generalized least squares fit by REML Model: flow ~ ec Data: rivin AIC BIC logLik 164.802 178.4841 -78.40098 Correlation Structure: AR(1) Formula: ~1 Parameter estimate(s): Phi 0.3111562 Coefficients: Value Std.Error t-value p-value (Intercept) 3.936472 0.5951170 6.614619 0 ec -1.106382 0.2228789 -4.964047 0 Correlation: (Intr) ec -0.999 Standardized residuals: Min Q1 Med Q3 Max -2.70663729 -0.58400432 0.03536558 0.33392867 5.01270171 Residual standard error: 0.3557397 Degrees of freedom: 228 total; 226 residual
Here I just please want to know how to interpret the results and what to report in an article. Do the
Coefficient results indicate that
ec decreases as flow increases and that this is significant? And what does the
Correlation (Intr) show me? Does this value of -0.999 indicate collinearity between the two variables and make the model invalid? And what do the results from the
Standardized residuals indicate?
Thank you in advance.